Gdub:
I think you err in choosing your word - homophobes - which literally means "fear of homosexuals." Clearly, few people, if any, are "fearful" of homosexuals, unless the word is broadened to include "fear" of their influence in society. Note that I am making no moral judgment here; I am simply pointing out that the word "homophobe" is a misnomer, and is often used by the gay community as an "activist" word which actually serves to further "divide" them from "the mainstream."
Christians believe in a particular moral doctrine, yes. But even this is misunderstood - and often deliberately misinterpreted - by the gay community. Let me make two comments on this regard, the first of which requires a brief primer.
Christians believe that each of us has a "soul," which is eternal. That soul "inhabits" our mortal, temporal bodies for approximately 90 years, after which it is released to be judged by God, and lives "in eternity" in either "heaven" or "hell." Note that the correct meaning of "hell" is not what most people think - fire, damnation, etc. (which is reserved for very few) - but "eternal separation from God." Thus, we need to consider two "spheres" here: the temporal/mortal, and the spiritual/eternal.
God loves every single human being, regardless of their moral or other failings. And Jesus preached that unconditional love, forgiveness, compassion, etc. However, in the "Christian construct," there are two specific expectations put on us. First, that we admit that we are "sinners" (that we fail morally and otherwise), and "repent" for those "sins" (moral and other failings) by asking forgiveness through Christ's sacrifice. Second, that we make at least some effort to live as Christ did - to be "Christ-like" - by (i) practicing the main precepts of Christ's ministry (love, peace, forgiveness, compassion, humility, patience, charity, selflessness, service, truth), and (ii) at least attempting to avoid "sin," especially conscious, deliberate sin.
However, the unconditional love of God and Christ is only applicable to our temporal lives, in as much as there is no "judgment" during our temporal lives. But there will be a "judgment" for each person as our souls leave the temporal world for the eternal one, and that judgment will be based on our faith (in Christ) and our "works."
I have previously used the example of the adulteress who was about to be stoned when Jesus came along and told her accusers "He who is without sin, let him cast the first stone." And I pointed out that it did not end there. Jesus then asks her "Woman, where are thy accusers?" She replies, "They are gone." And Jesus says, "Neither do I accuse you. Now go, and sin no more."
"Sin no more." Note that Jesus did not let her off the hook: He forgave her for the sin that brought her to that moment, but made it clear that He did not expect her to remain in sin, because from that point on, her sin would be conscious and deliberate, and not just a "moral failing."
Which brings me to my second point.
There is no evidence whatsoever that there is a "gay gene," any more than there is a "serial killer" gene or a "wife abuser" gene or an "alcoholic" gene or a "drug abuser" gene, etc. (I am not comparing being gay to serial killing, wife abusing, etc., simply making a point.) Thus, homosexuality is learned behavior. It is not "innate": no one is "born gay." And even if the circumstances that cause one to become gay occur in very early childhood - and are thus deeply ingrained - it remains "learned," and can therefore be "unlearned," no matter how difficult or painful that may be.
That is why Christians consider homosexuality a "sin"; because it is a moral failure, even if it is perhaps the earliest learned, most deeply ingrained one, and thus the hardest to undo. And just as Jesus told the adulteress "Go, and sin no more," God does not expect you to "remain in sin."
Thus, there is no conflict or hypocrisy in Christians who love and accept gays, and yet believe that gays will be "eternally separated from God" if they "remain in sin" and make no effort to change. It comes from the understanding of the difference between the temporal world - in which Christians are expected to live "Christ-like" lives, including love, forgiveness, compassion, etc. for all people, regardless of their moral and other failings - and the spiritual/eternal world that comes after.
I realize this is little "comfort" to you, or to other gay members here. However, as noted, I am simply explaining "how it works" within the "Christian construct." You are, of course, free to reject that construct, or find it exclusivist, narrow-minded, etc. I simply wanted to explain how it is that Christians - even "good" (non-judgmental, non-condemning) Christians - can, on the one hand, truly love and accept gay people - without a hint of "homophobia" - yet on the other hand believe that, unless gay people make some effort to change, they will be eternally separated from God on "judgment day."
Peace.