What is Craig Parker Haldir's sexual orientation?

Yes, he is. Here is a link to an interview he gave at one point where he mentions that he is gay.

http://www.streettalk.co.nz/forum/discussion/3682/craig-parker-guy-warner-interview/

Or you can try this link

http://img.photobucket.com/albums/v129/lea_ysaye/seven/no_nice_guy1a.jpg

Fourth column at the bottom.

Yes. He is openly gay.He did confession in a magazine"Sunday Herald" (NZ)-2008.

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It appears Parker first publicly discussed being gay in an interview with New Zealand's Sunday Herald back in 2008. Regarding his sexuality, the very private Parker told reporter Shannon Huse that as a gay man, he doesn't care what people say about his sexuality and that:

It's jut not an issue for me. I just don't get why an actor would want to reveal their secrets, hopes and fears to a magazine or newspaper. I know what the magazine gets out of it, but not the person. If you are doing publicity to increase your self-confidence then you are really in trouble. It's important to keep some privacy. Your friends and family are the people you reveal yourself to. They are the ones who should have real access to you.