I would definitely let my boyfriend go to a strip club. It's his life, he can do what he wants, and in my experience the women in strip clubs are generally just not that into it- and why should they be, since they are being paid? Obviously the good ones fake it well, but they are hardly going to be looking at their customers and going 'yeah, I like him, I'm gonna take him home with me!'
My boyfriend went with three of his mates to a strip club a few months ago, all of whom had girlfriends. My boyfriend told me in advance and I said I was fine with it as long as he behaved himself. One of his friends told his girlfriend while they were there and she went mental so he bailed. The other two just lied to their girlfriends about where they were. Why would you want to be in the kind of relationship where your boyfriend feels he needs to lie to you so he can go and have fun with his mates?
I trust my boyfriend more than anyone else so I believe that he would never do anything untoward, and in fact, on the aforementioned evening he rang me up and told me that he didn't like the strip club because it was really soulless (as well as complaining about the lack of size of the strippers' assets, but we'll let that one lie!).
If you disagree with a strip club because you think it's immoral, fine, but otherwise I think people who won't let their partners go are generally insecure about their relationships.