Its possible in non Judaic religions - Hinduism, Buddhism, Taoism, ancient celtic or egyptian faiths, persian faiths. Not possible with Christianity, Islam and Jews.
It's been over 10 years since I considered myself a christian. These days I tend to think of myself as a "philosophical mystic".
But from what I learned about the Old and New Testament and also Jewism, nowhere in the OT does Jahve really condemn homosexuality, for a large part it seemed to depend on a certain interpretation of the OT.
As for NT, well, it seems to be clear that Paul spoke openly against homosexuality - and he was the only one to have a word on this issue. But then again, when I examined the life of Paul, it soon became clear to me that he was a hateful bigot before he was turned into christianity and he was a hateful bigot after his conversion. It always mesmerizes me how on earth his writings ever were accepted as a part of the Bible. My only theory is some kind of a corruption and favouritism analogous - but by no means similar - to that of how the Borgia family ever came to rule the catholic church.
Without giving any opinion of the validity of the Judaic God or christianity, I can only say that throughout the history of christianity poor, even erroneous, judgements have been made concerning the foopundations of christianity, and from what I remember (I haven't really cared to study much after leaving my church), there have been notable theologians and scholars who would agree with me on this.
So, it might not be impossible in theory to be a homosexual christian, but it may very well be impossible for some individulas to practice christianity because there is still a lot of confusion about the issue in christian society and it may be difficult to find a church that accepts homosexuals. Therefore, in practice, worshipping the christian God may become unbareable at some point due to the view of your fellow christians, sadly.
As for the other Judaic religions, I don't know enough about them to say yay or nay, but it might not be as easy to practice other religions either as a homosexual, those that seem to be more "open-minded" for the exact same reasons: for example, if you want to really practice Taoism as a religion, and not just ponder about its philosophical aspects, you are bound to run into some nasty obstacles if you're a homosexual sooner or later, because some Taosits do believe homosexuality is unnatural (as would some hinduists etc. I'd assume) and they might not be shy to share their views with you.