I don't get rashes or infections from riding, but...
I just put a dab of hypoallergenic hand/body cream on my private parts area before I ride.
If I don't use anything, I find that my girly parts can get sort of stuck into one position and that is uncomfortable after a while. If I use a bit of cream/moisturizer however, then my girly parts can better slide around and rearrange themselves as needed during the ride and it's way more comfortable. (sorry, no other way to describe it!) I don't do 100mile rides yet(!), but this helps for my 20-40 mile rides. I don't want to use any petroleum based stuff like Vaseline or BagBalm, as I don't like that petroleum stuff for my body and also it won't wash out easily, too greasy.