This passage is always misused, as Peter warned about Paul:
2Pe_3:16 As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction.
If you consider the words carefully in 1 Timothy 4, and understand the words used, like "βρωματων" (just means foods), and the words "which God hath created", as a reference back unto Genesis, wherein that which was for "meat" (Genesis 1:29-30) was plant-based, and nothing of animal flesh.
It is speaking of that false religion (Revelation 17) which imposes upon mankind unscriptural (notice, not of God's word) restrictions and all manner of 'fastings' from that which is actually from God to be "received with thanksgiving". This system, stands inbetween God and the persons, and imposes unscriptural restrictions. It is not enforcing scriptural restrictions, but through their vain tradition, negating God's own words.
Notice the connecting words:
1Ti 4:5 For it is sanctified by the word of God and prayer.
That which God created for food, must be found to be in the Bible, and thus "sanctified" (set aside by God) for food, and then also "prayer". Praying over that which was never sanctified for food (such as pig, etc), is merely mockery to God.
That same counterfeit system (Revelation 17), also imposes between God and mankind in regards marriage, in that it restricts ("forbids") marriage amongst certain peoples, and there is a system on earth which forbids its priest-class to marry.
1 Timothy 4 is not in favour of 'the diet' many eat today, and claim God sanctifies.