No, it doesn't. YHWH (Yahweh) outlined for us in Leviticus what He considered "clean" and "unclean." How does eating at your unbelieving cousin Joe's house suddenly reverse that? How did the death of Yeshua reverse that? He was our final SIN sacrifice who - contrary to popular belief - NEVER negated His Father's Divine Instructions in Righteousness (Torah).
The answer is: It didn't. Yeshua Himself ate only kosher foods. You never see anything in the Bible that suggests otherwise. Let's take a look at "the short answer" from an excerpt from Welker's book, "Should Christians be Torah Observant?"....
"Unclean" animals/birds/fish are those that are carnivorous, those that are scavengers, those that eat roadkill and whatever they can scrounge, and those that eat dead things off the bottom of the ocean floor. YHWH wants His people to be "clean" from the inside-out, in thought, word and deed...Eating the "garbage disposals" of the world not only makes our insides filthy, but also serves to cause us to be disobedient to God! The bottom line is: God commanded us NOT to eat "unclean" things. (This Wikipedia article contains some valuable info concerning the "kosher" issue.)
YAHWEH never said pork, shellfish, etc. were food. People called these animals food in rebellion against God....
The passages in Romans are dealing with animals YAHWEH gave us to eat and whether they are ceremonially clean and can be eaten at that time. Even in Peter's vision (Acts 10:10-28, recounted in Acts 11:5-18), Peter would never have eaten the kosher animals that had been in contact with treif (non-kosher) animals. The vision was to show that, as Peter knew which animals were clean and which were not because God had shown him, Peter was now to accept the Gentiles as God had shown him they were “clean”. The full narrative in Acts 10 & Acts 11 show that this is the correct interpretation and what the vision was all about....
...Eating food that was dedicated to other gods shows allegiance to the people and to the god it was sacrificed to; consequently, it is forbidden.
Anyone who doesn't eat of things "sacrificed to idols" is also being careful to not convert cultural polytheistic values into a Messianic lifestyle. This is not solely about the abstention of certain foods; there are many aspects of community, and status quo values that are attached to things "sacrificed to idols."
The company a person keeps is also being addressed here; this distinction regarding food brings opportunity to introduce others to the Kingdom. This matter of eating things "sacrificed to idols" is so basic and foundational that it has the power to bring souls out of paganism, as do each of the Commandments of YAHWEH. To be a Kedoshim (Set Apart People), is Mashiyach (Messiah), every individual makes a choice to uphold Torah as the Word of YAHWEH, or not.
But false religion presents "alternatives" to the Word of YAHWEH; relativism, removing Set Apart distinctions to make convenient traditions so that people are not embarrassed by truth. Y'shua and his disciples never ate treif, nor things sacrificed to idols; neither would they eat "whatever" was set before them, which is simply a religious projection.....
Now, let's take a look at 1 Corinthians 10 in context:
1 Corinthians 10: 19. What then do I say? That an idol is anything? Or, that an idol’s sacrifice is anything? No. 20. But that what the Gentiles sacrifice they sacrifice to demons, and not to Elohim. And I would not that you should be associates of demons. 21. You cannot drink the cup of our Master (Y'shua) and the cup of demons; and you cannot be partakers at the table of our Master, and at the table of demons. 22. Or, would we provoke our Master (Y'shua's) jealousy? Are we stronger than he? 23. Everything is in my power; but everything is not profitable. Everything is in my power; but everything does not build up.
24. Let no one seek his own things, but also the things of his fellow-man. 25. Whatever is sold in the flesh-market, you eat, without an inquiry on account of conscience: 26. For the earth is Master YHWH's, in its fullness. 27. And if one of the pagans invite you, and you are disposed to go, eat whatever is set before you, without an inquiry on account of conscience.
28. But if any one will say to you, This meat is derived from a sacrifice; don't eat it, for the sake of him who told you, and for conscience's sake. 29. The conscience I speak of is not your own, but his who told you. But why is my freedom judged of, by the conscience of others? 30. If I by grace partake, why am I reproached for that for which I give thanks? 31. If you therefore eat, or if you drink, or if you do any thing, do all things for the glory of Elohim. 32. You be without offense to the Jews and to the Gentiles, and to the assembly of Elohim: 33. Even as I also, in everything, please every man; and do not seek what is profitable to me, but what is profitable to many; that they may live. (AENT)
 Actually "Pagans." By calling these people khanpa rather than aimmeh, Rav Shaul is making a clear distinction between the Gentiles who are learning Torah under his leadership from their fellow residents who are still steeped in anti-Torah lies and polytheism.
 "Whatever" is sold in the marketplace refers to meat that has the potential of being "sanctified by the Word of YHWH." Rav Shaul did not give license to buy pork or unclean meat from the marketplace; see 1 Timothy 4:5. In addition Rav Shaul says in 1Cor 10:25: "Eat whatever is sold in the meat market without raising questions of conscience." (Stern's Complete Jewish Bible). The context of this verse is important. First, of course, Rav Shaul is not saying here that "all food is okay to eat." The fact that Rav Shaul lived a kosher, Torah observant life amply supports this. Here, Rav Shaul is talking to the Messianic community of Corinth, and he and they know to only eat Kosher. So this verse is not permitting the eating of pork, or shellfish, or anything that is not "food" as declared by Yahweh. Secondly, in this part of chapter 10 of 1 Corinthians, Rav Shaul returns to the topic he introduced in chapter 8 - that of food sacrificed to idols.
Rav Shaul is explaining how the food that was prepared has no hold on you - that since you are living a life of obedience to the Word of Yahweh, then the food that Yahweh permits, provides the same sustenance for you as it would if you knew its "chain of custody" (to use a legal phrase - meaning, if you could trace the path of the animal from its owner to the meat market, and you therefore knew it was handled entirely kosher, the meat has the same value to you and your body as it would if you were not able to trace its chain of custody. However, if you find out that it was sacrificed to an idol, even though you could still eat it because you know that that sacrifice possesses no power over you, you should not eat it so as to show the "unbeliever" (vs 10:27) serving it to you, in a teaching opportunity, that his sacrifice was not valid and that you will not participate in what the unbeliever intended it to mean. See Rav Shaul's own clarification of this in the verses just prior to 1 Cor 10:25. In 1 Cor 10:19-21, Rav Shaul says you do not want to partake at the table of our Master Y'shua and at the table of demons - instead take courage and show the unbeliever the error of their ways.
 All Believers can determine whether meat is unclean pork or shellfish or whether it could be sanctified according to the Word. In this case khanpa designates "Pagans" and refers to whether the meat was sacrificed to a pagan idol. If someone informs you that the meat came from an animal that was sacrificed to an idol, do not eat it. See also Acts 15:28, 29, Exodus 34:15, this is no license to eat unclean food.
 Conscience refers to the discernment of right and wrong, based on Torah as the Word of YHWH. "Conscience" among the household of Faith is neither arbitrary nor variable, but a “group conscience” of the "Kedoshim" (Set Apart people). As Torah is being written upon the heart, Jeremiah 31:33, each soul is to recognize and support the work of the Ruach haKodesh within the Body. Paul is not at "liberty" to break the Word of YHWH and eat meat sacrificed to idols. He is addressing the frail and immature "conscience" of those who struggle to leave paganism. When a Believer voices Torah conscience, the rest of the body is obligated to support them, even if some think otherwise. Paul refers to the Believers in Corinth as carnal babes who can't digest solid food and who are struggling to receive truth; they are contentious and walking in the flesh (1 Cor 3), much the same as the modern Christian church who uses these verses to endorse violation of Torah, which is simply a poor attempt to "justify" the weak carnal flesh.
 If the food appears kosher and you have prayed unto YHWH, why should you be reproached if you didn't know the full quality of the meat? If the host knows about removing blood, and states that precautions have been made, and you pray that it be acceptable, is that not enough? Otherwise a person would be required to be present when the meat was prepared. Nowadays, kosher food companies supervise both the slaughter and the preparation of meat in the kitchen. Absent these things, the next best thing is to do the best you can, offer a prayer, and do not let worry ruin the meal or offend a well-meaning host who gave it their best effort.
 Diplomatic and kind to all, but never teaching against Torah. See 1 Corinthians 9:21. Only a fool would think Rav Shaul to be a man pleaser, as though he postured himself as a social butterfly to win popularity; this thinking is merely projecting one's own ideals. Rav Shaul preferred the Malchut Elohim; he could have been a "big boy" in the "traditional" Jewish world, but he left it behind for Mashiyach.
So how can I make sure I don't eat anything "unclean" in today's world?
This is hard to answer because in today's world it is hard to find "real kosher" foods and we can only do what we can do. Today, it really is a "heart issue" because, unless we stop buying anything in grocery stores and grow our own food and raise our own animals and butcher them ourselves, there's no way we can be sure that we're not eating something unclean....
Being kosher today is a matter of being careful that, wherever we go - say, to McDonalds - that we purposely choose only beef and beef products or "clean" fish (as outlined in the Book of Leviticus), and stay away from pork. Or picking only "clean animals" at the grocery store. Once you get the meat home, you can "kosherize it" yourself by either pouring salt all over it and leaving it for about half an hour (salt draws out the blood), or by putting it in water and boiling it for a couple minutes in the microwave. YHWH just wants us to do our best to obey, that's all. We cannot "wrap ourselves around the axle" and get an ulcer worrying about everything little thing we eat because the stuff that comes off the grocery shelves contains countless ingredients that are often impossible to discern.
You can Google "kosher foods" to find lists of "unkosher" foods, such as Jell-O (gelatin contains horse hooves to make the "gel"), and things that contain certain dyes which are made from certain "unclean" bugs, etc. The list is endless and, after awhile, you'll just begin to "know" what to look for at the grocery store....
If you still have some doubts, please take a look at what else Paul wrote here:
2 Corinthians 6: 16. Or what agreement has the temple of Elohim with that of demons? For you are the temple of the living Elohim; as it is said, I will dwell among them, and walk among them, and will be their Elohim, and they will be my people. 17. Wherefore, you come out from among them, and be separate from them says Master YHWH; and don't come near the unclean thing, and I will receive you; 18. And will be to you a Father, and you will be sons and daughters to me, says Master YHWH the Almighty.
It would be impossible to eat something unclean if you are not even supposed to touch it.
May YHWH richly bless you for trying your best to do HIS will!