Is it rude to call a gay person "homosexual?"

Well, I suppose it's slightly better than gay, which is now used derogatorily quite often, whereas homosexual has a more scientific detached feel to it.

However, I wouldn't say that makes it ok to use in a context like that—it makes it feel like you know them only by their sexual orientation and not by who they are as people, so it is still sensitive in that respect. It would be more acceptable to use a different quality—perhaps answering "him" while gesturing in his direction, or perhaps "the one working on the [so-and-so] project"; these alternatives make it seem like you're not concentrating on sexual orientation.

Oh, for heaven's sake. Speak to your Gay/Homosexual co-worker and ask HIM what language he prefers and why. Strike up a genuine friendship and get some real answers to your question. He probably won't bite if you approach him like another human being and not merely as a member of some group.

Many gay people, including myself, find the word homosexual somewhat offensive because of the way it has been coopted by professional anti-gay activists such as the National Organization for Marriage and the Family Research Council. One News Now, a news website run by the homophobic American Family Association, once got into trouble for taking a AP press release about the sprinter Tyson Gay and publishing it as "Tyson Homosexual". They have an automatic filter which converts gay to homosexual. Why do you think they feel the need to have that filter? Why are homophobes uncomfortable with the word gay?

It's because gay and homosexual don't mean quite the same thing. Homosexuality is an orientation. A gay person (note that both words can be used as nouns, but many gay people are uncomfortable with that) is comfortable with his sexuality. He has established, to borrow the language of the religious right, a "gay identity".

Gay news blogs such as Box Turtle Bulletin and human rights organisations use the word gay throughout their writing.

Words mean things, even if the difference is subtle; and this difference in usage has an effect:

A recent CBS/New York Times poll found that 70 percent of Americans are in favor of gay men and lesbians serving in the military. Hooray for progress! Unfortunately, the same poll found that only 59 percent of Americans are in favor of homosexuals serving in the military.

Salon.

Mike Christian's answer is therefore shown to be wrong. The word homosexual is not "more appropriate". It's not used in a human rights context; it's not used in a cultural identity context; and it's falling out of favour in a medical context (they use "men who have sex with men" instead, to cover all bases). The only context in which the word homosexual is still commonly used is an anti-gay context. Avoid it.

I can't speak for your co-worker, but the part that would have bothered me about that statement was that you were identifying someone to a person who didn't know them by something that is logically a non-physical characteristic.

So basically you are asking your friend (and anyone else in earshot) to look around for someone who "looks homosexual".

Yes, that would have bothered me too. I have enough trouble fighting the innate bigotry society has instilled in me as it is, without having to deal with others inviting me to indulge in it.