You will not make the world a worse place by telling people you appreciate their appearances.
I ask, I don't care if I know the girl or not. I avoid asking teenagers or early-20s because I don't want to weird them out too much. Unless I know them, in which case I'll just ask.
My experience is that every person, male or female, will be happy to take the compliment and to offer help for finding a particular garment, even if they don't remember or know where something was purchased (I've often asked and gotten "It was a gift, I have no idea, but I wish I knew because I'd shop there").
What I never find is when I like something a GG is wearing, she never tells me it was a gift from her husband. The person gifting is usually another GG. Interesting, that.