If you just want to befriend me, does it matter what I look like? Yeah, it does. Well, I'm superficial, so are you. If you feel that I'm not presentable to be your friend, fine, you stuck up sob. We all have the rights to choose our friends, and it's not wrong if we want to surround ourselves with goodlooking friends. Vain as it is, we just can't help it, it's in our bones. Gay pride... haha.
But it is a totally different matter when you refuse to show your picture and expect people to accept you as who you are. Nobody are that lacking in friends to accept such bullshit. Come on, so you are not running for Manhunt, nor does 99% of the rest of the world. A person who has confidence in himself looks better then those with just good looks, just barely anyway.
Again, if you just want to befriend me, does it matter that I am single or attached or having multiple partners? Oh, you fear that you might fall for me one day because I'm such a good guy that you don't want to be the possible intruders into my beautiful relationship. Well, in that case, I'm flattered, I'll let it go this time. Sometimes we just overestimate our charms. If the guy that is attached can so easily dump his current for you, he can be as good as it gets. Those who are really committed doesn't budge so easily, they are more often a sore to the eyes instead when they are together. Of course if you found yourself falling for a happily attached friend, then at least you have a standard reference for your future prospect. You can also compare yourself to the so-called competitor and improve yourself accordingly. Think in terms of game theory, there is no reason why it can't be a win-win situation.
And if I am someone who have multiple partners, does it matter what my private life is to you? Unless you want to be one of those partner. And if your fear for sexually transmitable disease, insist on using condoms then.