My jodphurs have the suede seat on them so you don't really notice it. Also, I don't really care. I'm there to ride my horse and do the best I can. If it came down to me or another person winning or loosing because of a pantie line and I lost because of it, I would be protesting. Not because "wah wah, I don't have a pretty ribbon
" but because that's the dumbest thing to loose from.
If you're that concerned, you could try a g-banga or the seamless undies. Oh, or the ones that are like bike shorts that "hold everything in". I know people that use them when competing and they work.