With lesbians, gays, and bisexual service members now having equal opportunity protection in the military, one question that I hear all the time in the Special Warfare community is, "How do I work with somebody who is gay, or I think is gay?"
As a gay Navy SEAL, I speak from experience. That "gay" operator is probably just as, if not more uncomfortable than you. They most likely spend their life walking on eggshells mindful of what they say and do (especially if their in the closet). As you're well aware, unit cohesion is essential in that environment, so having somebody feeling that way can damage unity. As a straight operator, you can do things to improve that atmosphere. Something as simple as voicing your support of gay people in your unit will move mountains for them.
"What if it's against my religion?" Despite what your religious leader said, it's not a choice. Just like being straight was not a choice for you. Nobody is asking you to change your beliefs. You don't have to choose between the two. You just have to let a person do their job, and create an environment that permits it.
Try and imagine it from their perspective. They've probably been struggling with it for years. Chalking it up as a "Phase" and even going so far as being in a heterosexual relationship. Think about how miserable that could be. Imagine being in a gay relationship as a straight person, safe to say, you probably wouldn't like it. Accepting whom you are and coming out is really- really fucking hard. People kill themselves over it all the time, so remember that when they decide to tell you. Again, you don't have to agree with it, but respect the enormous amount of trust that they are putting in you and the team. It is important to note, this is not the time to try and convert them to your religion. What is important, is they know you're still picking up their six, even if you need time to wrap your head around it.
It may take awhile for you to accept this person, and there is nothing wrong with that. Acceptance doesn't happen over night, but try and keep an open mind, and avoid the shit talking. I would say to avoid the gossip, but I know how impossible that is; so just avoid being negative. If somebody is a solid operator, they deserve the same respect you would give anyone who's squared away.
Lastly, ditch the stereotypes. This isn't some 1980's movie. We're not sneezing glitter, or waiting for you to drop the soap. The majority of us want to do the job, do it really well, and get home to see our loved ones alive- just like you do.