First of all, when I look at what the two photos depict, I don't think in terms of liberalism or conservatism, but in terms of sodomy and murder which are sins against the Commandments of God, but that's just me.
No, that's what you are supposed to see.
This exercise is solely about the gedanken experiment of mixing those two groups and seeing which group would actually hurt the other.
As a conservative you can see both groups as wrong and evil. That's consistent.
By the very practice of what the sign in Photo 1 denotes, homosexuals are slaughtering themselves en masse. Homosexuality in an of itself is a very deadly practice.
I myself find the sign in photo 1 offensive. But I defend that man's right to say whatever he wants as long as he doesn't threaten or defraud others with his words.
Also, homosexuality is rampant among men who profess to follow Islam.
Yes. That is also a valid point.
Saudi-Arabia, for example, has such strict laws against men and women meeting each other than many places that would cater to both sexes in normal countries cater only to men in Saudi-Arabia with the result that men meet other men all the time and have no chance to meet women.
I assure you that such a scenario is as frightening to me as it is to you.
If I found myself working in a place where I meet only men and otherwise only frequent places where I meet only men, I would think that something is wrong with my life. Yet this is a typical lifestyle in many Muslim countries where I think it encourages people to live in such a world.