Whew, here we go! Grab hold of something, it's gonna move quickly:
(I believe the problem with the common interpretations of these verses is that they don't consider the immediate context and they bring in opinions about matters foreign to the text. Then these verses are all used to justify each other, but you can't justify one passage by another misunderstood, de-contextualized passage. I will attempt to show what I believe to be the proper context for each. The result will be that none of the verses can be used to support each other. All of this is up for debate and I imagine this will start a firestorm!)
Mt. 15 -- The Messiah was addressing ritual hand-washing, which was a Pharisaical rule and not a command of God. V.15:10 must be understood in this context. He certainly didn't mean we can consume anything because that would include human flesh, blood, etc. And if He was teaching that we can consume anything, then He would have been in direct violation of God's Law. The evidence that He wasn't teaching against the Law: The Pharisees didn't immediately arrest Him! Also, 10-15 years later, Peter (who surely was a witness to this event) seems completely unaware of this "supposed teaching" that He can eat or drink whatever he likes (cf. Acts 10, and below). The Messiah here also chastises the Pharisees for putting aside the commands of God, but some today believe He Himself put aside the commands of God with this teaching? Huh? In Matt. 15:20, the Messiah provides the interpretation of his parable (and yes, V.15 calls it a parable, which are not often literal teachings):
"These are the things which defile a man, but to eat with unwashed hands does not defile a man." Let's let the Messiah do the interpreting for us instead of creating our own interpretation.
Mark 7 -- Same story as above. V.19 is highly contested in terms of what is the best translation. The KJV renders it being about biological processes:
"Because it entereth not into his heart, but into the belly, and goeth out into the draught, purging all meats?" "Thus He declared" is not in any Greek manuscript. Even if it's best rendered as Him "declaring all foods clean," unclean meats were not considered food. Again, the evidence: The Pharisees didn't immediately arrest Him, and Peter clearly did not interpret it in this manner. Do we know better than Peter, who walked with the Messiah? The Messiah already provided the interpretation of this parable in Matt. 15.
Rom. 14 -- The specific issue causing disunity in the community is not the Lev. 11 dietary instructions. V1. says it's about disputable matters of opinion. When did the clear commands of God become disputable matters of opinion? Paul clearly defines it for us as vegetarians (V.2) and possibly those who abstain from wine (V.21) on one hand, and non-vegetarians and possibly wine drinkers on the other hand. All of Paul's statements must be understand within the context that he sets up and about the specific debate at hand, including Rom. 14:14. The issue influencing believers in the Roman community is likely meat sacrificed to idols, or possibly asceticism (or both?).
Heb. 9:10 -- Read the whole chapter. The context is priests and temple services from start to end, which include meat and drink offerings. This has nothing to do with what you, a non-priest outside of temple services and offerings, should eat or drink.
1 Cor. 8 -- The context is "eating of those things that are offered in sacrifice unto idols" (V.4). VV.8-9 are about this narrow aspect alone. This was a huge deal and caused some to become vegetarians, as indicated in Rom. 14. This is not about the Lev. 11 dietary restrictions.
1 Cor. 10 -- Same context as above: meat sacrificed to the altars of idols. Some people refused to purchase meat from the markets for fear it had been offered in pagan temple services. You could never know, so it became a "disputable matter." In VV.25-29, Paul is saying not to worry about it. You can't know and an idol is not a thing anyways. Again, this is not about the Lev. 11 dietary restrictions.
1 Tim. 4 -- Paul qualifies the meats from which people will improperly command to abstain as "sanctified by the word of God and prayer." Where does the word of God sanctify meats? Lev. 11 (and Deut. 14)! Unclean meats are not sanctified by the word of God and no amount of praying will do anything about it. Keep in mind at the time of this writing, there were no other written, assembled Scriptures. And Paul didn't know he was writing "letters of the Bible." In the end days, people will teach not to eat even clean meats. They already had a problem with this in the first century (cf., Rom. 14 and the vegetarians there). The context is teachings of men, not God. Abstaining from marriage is a teaching of man. Abstaining from clean meats sanctified by the word of God is a teaching of man. Can you think of any modern day "church" that teaches these things as commands of God? I can!
Oh, you forgot a couple!
Acts 10 -- Peter's vision is about people only. There is no lesson about diet here. The evidence? When Peter retells the story twice in the coming chapters, he provides for us the correct interpretation: Gentiles are now cleansed by the Holy Spirit after coming to faith. He never once mentions anything about dietary restrictions. When he later tells his Jewish brethren in Jerusalem the same story, they all shout praises about the Gentiles now being cleansed. Not one of them responds about dietary restrictions. Odd right, seeing as how this would have turned their whole world upside down! But that's because no one interpreted it that way! Let's stick to the interpretation the NT writings provide instead of inserting our own which is foreign to the text.
Col. 2:16-17 -- The text never explicitly says the people
weren't keeping these things. Read the entire chapter, none of it is about God's commands. What we see are a lot of probable references to asceticism and/or proto-gnosticism. Both were huge problems in the first century that had infiltrated both Judaism and Christianity. The Biblical holy days are feast days, to be celebrated in gladness with food and drink! Ascetics taught that such indulges were sinful. They abstained from food and drink, abstained from sex, lived in poverty, etc. Paul says not to be judged for these things because they are a shadow of the coming things and are the body of the Messiah! That's a good thing! They are intimately connected to Him and the events related to His first and second coming! In Col. 2:14, Paul explains that the Messiah took the charges against us (NOT the Law) to the cross, so don't let these ascetic heretics bring false charges against you!
Nowhere does Paul or anyone else come close to saying anything like: "Listen, we're gonna talk about clean and unclean meats from the Law. Now you've heard that you can't eat unclean meats. But I'm telling you they're wrong -- you can eat whatever you like! So bring home that pork roast from the market, gather Jew and Gentile around, and feast until your heart's content!"