Assumptions that need to hold, for homosexuality to be objectively wrong in a “Christian” context:
(1) There exists only one unique objective morality that everyone should adhere to.
People will never agree on this, because it just depends on how “morality” is defined.
(2) God’s morality is what (1) refers to.
This assumes that God is actually “good”, whatever that may mean. It is difficult enough to argue conclusively that “God” exists. Even harder to argue that only one “God” exists. And far harder to argue that the one “God” that exists should be responsible for deciding what “good” is. Because surely God is not “good” simply because he is all powerful. Power doesn’t really relate meaningfully to morality. Even if you grant that God is omnipotent, omniscient, omnipresent, it still doesn’t automatically mean that such a being is necessarily going to be “good”.
(3) The God described in the bible is the correct God.
There all kinds of reasonable, non-supernatural explanations for why people would have long-standing organised religions around the collection of ancient books collectively called “The Bible”. The mere complexity of the issue, encompassing pretty much all kinds of fields like History, Psychology, Science, Philosophy, Literature, Linguistics, etc., suggests that it is humanly impossible to be reasonably sure that “The Bible” legitimately and meaningfully describes the correct God. People who claim otherwise are just woefully ignorant of the intellectual, scientific, etc. limitations of humans in general.
(4) The bible accurately conveys what God wants us to know.
A whole bunch of ancient people writing ancient documents that later got copied many times resulting in different copies whose contents vary significantly depending on which copy you refer to, from which hundreds and thousands of years later a bunch of people invented their own idea of “The Bible”, and voted (not unanimously; votes were sometimes split almost 50-50) to decide which of these ancient writings were to be collectively known as “The Bible”, with different religious groups having different “Bibles” comprising significantly different sets of ancient writings.
So many human hands were involved in making “The Bible”, so that realistically there’s no guarantee that God was 100% happy with this process. If anything, God probably has much to say about how large groups of people naively assume that “The Bible” contains 100%, without error, what God wants them to hear. Oh hey, let’s pick and choose which ancient writings we like, create a committee to vote on it, and conveniently declare that the resulting “Bible” is exactly what God wanted!
There is also the question of how “The Bible” is supposed to be read. Because words mean very different things depending on what context you think the text appriopriately belongs to. E.g. “I love cow” can variously mean I love my pet cow, or I love to eat cows. So even if the bible is 100% word-for-word without error, where are we going to find the 100% word-for-word without error documents that give us a full picture of the context in which those words were written? And where are we going to find the 100% intelligent human being who can digest and analyse 100% of that information, and produce a 100% reliable “biblical truth”?
Just any one of the above assumptions being wrong is enough to topple the elaborately crafted “Christian” idea that homosexuality is objectively wrong.
Furthermore, it is highly unlikely that human beings have the intellectual capacity, nor the material evidence, to reliably justify any one of the above assumptions.
Hence, the whole “the bible is magically 100% true and we should absolutely rely on it as the epistemological foundation for everything” idea is probably nonsense.
Which is why Christians (especially the conservative/fundamentalist types) tend to appear so intellectually deficient to much of the outside world.
By the way, I’d rather rely on the bible for actual “wisdom”, i.e. learning meaningful principles through the bible text. Said principles are supposed to make sense to our finite human knowledge so that we can meaningfully apply those principles to our daily lives.
Just simply insisting that the bible is 100% true, doesn’t really do us any good, if we are just deriving “statements of faith” that don’t really make sense, or that we feel like we have to obey out of mere obligation to some all-powerful being who will reward / punish us accordingly.
“Taste and see that the LORD is good” (Psalm 34:8) is very different from “The LORD is good because the bible is 100% true and you should just shove God down your throats even if you don’t really understand how it’s supposed to work.”