PatriarchyPersonified - great name.
To be honest some people see it as just 'something that you do on a stag do
I guess working there is just something women do for money and far less fun than going on a stag do.
In terms of the girls who work there, again in my experience, they are usually making a pretty good wage and have chosen to be there. Strippers aren't prostitutes (usually) and don't have to let anyone touch them.
I'm so glad you explained that strippers aren't prostitutes I'm not sure anyone on this thread was aware of that before. It makes no difference it is still men using and objectifying women. The women who work there may not tell you this but I happen to know that very few think highly about the men who are customers (regardless of their reasons ) and it often changes their perception of men.
This idea that all men who ever go to strip club for any reason are somehow scum is a bit much, I'm willing to bet that 99% of the people on this thread have partners/brothers/fathers who have been in a few strip clubs in their time.
I'll bet some have (not sure about the 99% but then I'm always dubious of men who come on and tell us that 'all men do this'). From your post only I don't think you are 'scum'. I don't think all men going to these clubs are 'scum' but I do think (as I said above) they are using and objectifying women and are contributing to pervasive negative perception of women throughout society. Again, I don't care much for their reasons for being there and while I might not think they are all scum I'm not afraid to judge them or tell them why I do.
For the OP, I'd say that the deal breaker shouldn't be that its a strip club, it should be the fact that her partner is insisting on going despite her protestations and won't discuss it or take her feelings into account.
While I agree with some of this it is the very fact it is a lap dancing club (not a strip club) that is the deal breaker so it is part of the reason the OP is upset - the fact he dismisses her feelings is just another equally important part. Lets not minimise what the majority of women think of this kind of things and the effects on women in general.
(I'm going to assume he is quite young,
He's in his 40s, the OP has said a couple of times I think. Shitty attitudes towards women and stupid male peer pressure isn't limited to young men apparently.
Please don't think I'm getting at you with this post, I don't think you are patriarchy personified 
but I do think men minimise what these issues mean to women because they simply cannot know the hurt (and anger) of being part of the population that is most used and abused in the sex industry and how this plays out in real life; in street harassment, sexual assaults from the serious to the 'hand on your arse because they can' type and the way we are spoken to. This shit affects us (women) all.