Definition of terms
Homosexuality in the New Testament appears to address this. Personally, I draw the conclusion that it is unlikely that the NT condones homosexual activity. It is, however, possible to honestly and sincerely hold this view of scripture, in which case, from a Christian point of view, it is between the individual believer and God, and "who are you to judge another man's servant?"
Are there any arguments in support of the claim that the story of Jonathan and David is not about homosexuality? Because if that's what it's about, I'd think it was really hard to use the Bible as an argument against homosexuality (...even granting the premise of the Bible as an authority).