The Bible says homosexuality is an abomination, but what is the harm? Furthermore, why are some instructions in the Bible, such as not to mix fabrics, not applied to Christians' lives today, but condemning homosexuality sometimes is?
Your understanding is not correct.
The word "abomination" does not have anything to do with something being "morally gross" or whatever.
The real reason to call something an abomination is if it is deformed and suffers because of the deformity. It is an abomination if it is like a suffering version of what it is supposed to naturally look like under normal circumstances, such as if it is living with severe genetic complications or if it is the product of close inbreeding (incest).
For example, if a dog is born and breathing is incredibly painful for it because it was born with a significant deformity in its muzzle or something, then the way its physical body has grown is an abomination because it is horrific and brings a lot of suffering to the animal.
So basically, the rule in the Bible which says "You shall not lie with a man as you lie with a woman, for it is an abomination" has absolutely nothing to do with homosexuals gratifying each other innocently. That is completely fine and natural, since animals also do this.
What that verse is talking about (but sadly, its vague wording has led to all of the hate and confusion) is if two men try to procreate a child together, by one of the men implanting an artificial womb. This then can lead to significant problems with the fetus, who can be born with extreme suffering because it was not carried to term in the nature-ordained cavity: the womb of a woman.
Note: Back in those ancient days, those rules from the book of the Levites (Leviticus) were being instructed to a clan of priest attendants who had no real concept of sex for pleasure or fun or amusement or joy. Sex was viewed by them like a duty of the religion, to procreate a next generation of Levites (who were a clan of Jewish humans, who performed functions like keeping the temple clean and waving incense around in preparation for the consciousness-based works of the higher priests). They also did not have a real word for sex or procreation, and so the only way to deliver the instructions was to describe it as "laying down with someone", similarly to how we will use the phrase "sleep with someone" to mean have sex with them. So that part of the Levites' book was basically just admonishing them to be careful about letting genetic damage come to their clan, since they wouldn't be able to perform their duties properly if they let themselves procreate deformed offspring - since to be a proper attendant for any kind of "spiritual work" you actually need a healthy enough brain.