If you could be completely anonymous would you have sex the same sex?

Anonymity is irrelevant. I'm straight, so - no.

If something just doesn't appeal to someone, what difference would anonymity make? I don't understand your question.

I wouldn't need to be anonymous and neither would she

Can't say I find anonymous sex particularly appealing.

If a person is heterosexual, I believe anonymity would be irrelevant to the case.

Been there, done that, and it wasnt anonymity I was concerned about, it was discretion and if my buddy would be able to keep the encounter between him and I.

It sounds like you are wanting to experiment but are concerned with being branded with the G card. Its normal for people, at some point in their lives, to be curious about the genders. Sexuality is not as cut and dry as the SLGBTQ labels.
Sex with another guy, whether you know them or not, does not make you gay. SERIOUSLY. Plenty of guys get drunk just so they can experiment and blame it on the booze or maybe have a three-way or if they are REALLY STRAIGHT they have a gang bang = lots of guys... one girl!
One sexual experience doesn't destroy your membership to the Straight club. Casual hook ups or encounters happen. If your intrigued, go and explore.
Realize = Your sexuality is not your sexual orientation. Being defined as gay, straight or bi (or one of the others) is for the individual to decide. Your sexuality is your own personal thing. Unique to everyone. So your sexuality is for you to explore and figure out.
But if your interests contradict how you define yourself then you are only going to confuse and hurt yourself. Live n the moment and remember that life is a learning experience. Your here to learn and understand YOU. so explore all facets of yourself.

nah men are horrible they're all hairy and rough

if it was totally anonymous and no one would ever know or find out I'm still sure I would pass. I like one penis and one penis only and that is my own. I just don't think that there is anything sexually arousing about another male. I don't even think I would be able to have a threesome with another male. I would like to end this by saying I don't have anything against homo sexuality. I say do what you enjoy and makes you happy. Dudes just don't do it for me.

Truly the anonymity is not the main factor. A better question might be "if you found the 'ideal' same sex partner, could you/would you have sex? in my case, the answer is yes.

Some people find sexual anonymity alluring. They like to fuck hookers on Halloween while they are both wearing masks.

Well, sex just scares me in general... doesn't matter who it is.