I've worn diapers in almost any kind of situation, be that out and about in public places, with friends or alone, or at work, even when out for some intensive video shootings. The more you get used to that, the more you realize it's not a big deal at all unless you make it so. It's actually convenient when out in situations where you don't have the time or opportunity to find a toilet! (If I'm not wearing a diaper, I may end up having to look for a toilet even every hour or so, or regretting not having worn, unless I badly dehydrate myself...) Sure, you may have to time changes, bring spares with you, and it may feel a lil sweatier than regular underwear if what you're doing requires lots of movement, but that's about it. There's really no reason to be paranoid about going out while wearing diapers, that's what they're made for after all, being worn and used by people!
As for clothing, I've spaced from suit and tie to jeans or shorts: as long as you don't go out with a doubleboosted Abena M4 under a pair of skin-tight leggings, no one is going to be the wiser. It helps that I like comfy fitting clothes to start with: since I started shopping for clothing while diapered I never came home from the shop to find that the jeans I had bought were a tiny bit too tight for me, which used to happen from time to time some years ago!
The only reason that kept me from wearing at school when I was in HS was that a few friends of mine used to pants me or slap my butt in good humor from time to time, which would have turned out in a quite funny (and embarrassing) moment had I been a crinklybutt
