I ride at a barn that is very mixed discipline, thankfully. I hate the typical atmosphere of one discipline barns that the boarders/coaches don't understand why you'd want to do anything but, and if you do, drama. I have only been at a barn like that once before, but have seen many others like that. I ride hunters, but I also do pretty much everything on my pony (including barrel racing in the past, trying to sort of get into that again).
When I am riding english I typically ride in my breeches - I have ridden in jeans before but don't feel as comfy and don't trust them on my saddle - and field boots, or my Hunter boots, and either a polo or another fitted tshirt tucked in. Western I generally do jeans and tshirt tucked in, and since I no longer have boots for western I generally just use my nicer muck boots or my Hunter brand boots.
For me personally, I generally cannot stand to have my tshirt untucked, or my hair showing from under my helmet. Just a personal pet peeve, but that has nothing to do with discipline, I don't care what discipline I am doing, it bothers me either way - no idea why though lol. I'm very OCD in general though, so. I have no problem if someone else wants to ride in jeans or whatever though, NGL I have done it more than once.