I don’t think homosexuality has much to do with logic; if we are talking about homosexuality and the Bible, the title of the threat should be ‘Homosexuality, Interpretation, and the Bible’, since the condemnation of homosexuality by Christians comes down to how they interpret certain Biblical statements on the matter.
Interpretation depends on the sort of assumptions and approaches you take to the text in question. This is the case in any problem of interpreting a text, be it a legal document, a book, a poem, a philosophical argument, and the Bible.
I think prima facie, it is clear the Bible does view homosexuality as wrong. The focus appears to be on homosexual acts rather than orientation, since the writers did not face the modern situation, but rather the situation in their own time, where homosexual acts occured in connection with practices in non-Jewish religion and culture (the Greeks for example). Clearly the writers of the scriptures felt homosexuality is contrary to the divine will, at least where homosexual acts are concerned, but I think St Paul clearly things that both homosexual acts and orientation are perverse (but he connects this to the wider context of sin in general).
As to whether in itself homosexual acts are always intrinsically evil, it depends on what grounds you use to argue ‘yes’ or ‘no.’ Most secular moral philosophers seem to regard the religious condemnation of homosexuality as baffling, at least in the 20th century, but when Christianity was a major influence on philosophy, even philosophers like Kant still argued for the immorality of homosexuality, pre-marital sex and masturbation on pure natural law grounds not connected explicitly to either natural law derived from divine providence or scripture (as Aquinas did).
I think it is clear religious scriptures and traditions, in the monotheistic religions, do not approve of homosexual orientation or relationships. But whether such a position can be supported without appealing to scripture or theological traditions derived from scripture, is another question. I think given most serious arguments for God’s existence have either been demolished or thrown into very considerable doubt, we have to look elsewhere than religion and claimed revelation to answer the question.