jesus is not recorded to have opposed many other immoral acts either .. doesnt mean he is indifferent or even supports them in fact jesus clearly says "Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. homosexuality being one of those.
The same books that prohibit homosexuality prohibit eating pork and advice you to stone to death the children that don´t behave.
I said before: the reality is that Jesus acted and TEACHED different than the past texts, so not all of them should be deemed as moral if yo are a christian.
I agree, there are a lot of things that are immoral that Christ doesn´t specificaly speak against.
That said, you abide by the two major principles: love god, love others.
Now if you are a christian homosexual, you would naturaly not think you are breaking any of these two by being homosexual (because then you would deem yourself unchristian). If you belief that homosexuality somehow breaks one of this two (and I am sure you do) you would deem it unchristian.
But do understand your point of view is merely that: a point of view. And a very unsuported one at that.
So yes, you can be a christian and an homosexual. You can also have premarial sex and be christian. Again, Jesus never spoke against it, and it dosn´t damage anyone nor God . Christ only spoke against infidelity.