Well I have to admit that I would never wear what basically amount to knickers in full public view.
I think you're being unfair, some people just won't be comfortable wearing such skimpy clothing and you're putting them in a really difficult position by insisting on them wearing them.
Sport isn't about being 'fun and sexy', it's about being as good as you possibly can be and what you wear to cover your arse isn't part of that. Seriously, what you wear the the most trivial part of sporting activity.
I would say just let them wear what they want to, in time they may decide to switch to the briefs anyway, but if you force them into something they feel deeply uncomfortable with then they'll resent you for it.
Honestly, this whole situation looks like a mountain made out of a mole hill, if most people are happy to wear them let them, but you shouldn't force people to wear things that make them feel uncomfortable.