As long as you're okay with it, I don't see why not. But if you don't want to, he can't make you. If he tries to, then you have every right to say no and possibly end the relationship.
And thongs aren't bad. Some people may think that they are for sluts or something like that, but in reality they're just a piece of clothing that goes under your clothes so people won't really see them. It doesn't really matter.