If so, why do many ignore it? I realize there are many verses as well that state in the New Testament that nothing is to be considered unclean anymore, but that makes this verse stand out as particularly odd.
No. While a few portions of a Kosher diet are highlighted there is much missing ie. fish without scales and birds of prey.
From the immediate context we know that he's not trying to burden the audience from trying to earn righteousness from following the law.
10 Now therefore why do you put God to the test by placing upon the neck of the disciples a yoke which neither our fathers nor we have been able to bear? 11 But we believe that we are saved through the grace of the Lord Jesus, in the same way as they also are.” Acts 15:10-11
However I do not think we get a direct answer in the immediate context to the question, "Given that no animal is unclean, why place instructions about dietary commands in this letter?" My best guesses are that 1. the purpose of placing the restrictions would be to not cause offense in the sharing of the gospel to the audience and 2 it's just a solid practice for people to adhere to.
19 For though I am free from all men, I have made myself a slave to all, so that I may win more. 20 To the Jews I became as a Jew, so that I might win Jews; to those who are under the Law, as under the Law though not being myself under the Law, so that I might win those who are under the Law; 21 to those who are without law, as without law, though not being without the law of God but under the law of Christ, so that I might win those who are without law. 22 To the weak I became weak, that I might win the weak; I have become all things to all men, so that I may by all means save some. 23 I do all things for the sake of the gospel, so that I may become a fellow partaker of it. 1 Corinthians 9:19-23
The forbidding of blood comes from before the time of Moses :
But flesh with the life thereof, the blood thereof, shall ye not eat.
Genesis 9:4 - KJV
After the Flood, in a new arrangement, flesh is given men to eat, but not blood. In a world now cleansed with water, flesh is made available :
... my flesh, which I will give for the life of the world
John 6:51 - KJV
Blood is not given to unrepentant mankind to consume. The blood of the everlasting covenant is received by faith, Hebrews 13:20.
So neither blood, nor things strangled (instead of having the throat cut and the blood drained out) are permitted to the gentiles. This is not because of Jewish practice, it is because the commandment of God to Noah pertains to everyone on earth until the end of time.
Meats offered to idols is a matter of fellowship with idols which Paul makes even clearer to the Corinthian believers in the eighth chapter of First Corinthians.
Again, it is not a matter of Jewish practice, or custom, it is a matter of contemporary fellowship with local idolatry.