My girl wears in public fairly often, and is sometimes rather anxious about it.
We solve this in three parts:
1) Choice of diaper
When she wears in public, I put her in very tight-fitting pull-ups. They can't hold anywhere near as much liquid, however, so we're very careful about that.
2) Choice of clothes
Super skin-tight jeans are out, unless she wears a long sweater that will cover it.
Usually she'll wear leggings and then a skirt over that, or pants that don't fit as tight.
3) Mindset
Keep in mind the frame of reference people have around you. A couple and their young child that are out buying groceries don't care what anyone is wearing.
There are a select few that even have it in their frame of reference that anyone older than a toddler might wear a diaper, and they are either AB, DL or IC themselves.
If I spot something I think maybe might be a diaper on someone I don't know, then I won't point it out to anyone, won't yell it out and certainly won't comment on it.
If I spot it on someone I do know, I probably won't comment on it either, because I know it's an uncomfortable thing for most to have brought up.
To sum up:
People won't notice. If they do, they won't bring attention to it.
If the choice to wear a diaper is even in their mind, they're unlikely to make a big deal out of it. If not, they'll assume it's medical, and will absolutely not make a big deal of it.
One exception, though: Kids.
They're assholes, but accidentally so.
"MOM! IS THAT GIRL WEARING A DIAPER?!"
Everyone will ignore it and pretend it didn't happen, and the most embarrassed person around will not be you; It'll be that mom!