I do. Especially when the tag it in mechanically, but also when other people try and pigeonhole characters based on the baked in flavor.
Most onerously for me is the push to make sure rogues only get SA with certain weapons or the non-mechanical non-rule of druidic armor.
That's not quite what I'm referring to, though I can see where those would be issues.
I'm more referring to things like, for example, the fact that the Fighter has essentially no flavor whatsoever unless you pick specific subclasses (e.g. Rune Knight)--even the Eldritch Knight is practically devoid of any flavor whatsoever--whereas something like Bard or Paladin has a lot of flavor, but that flavor can be pretty easily ignored.
Bard colleges can be reflavored in a host of different ways, and despite the label on things like "Song of Rest" and the instrument proficiency stuff, the class isn't
required to do anything related to singing or music at all. Many think of it as such, but you could quite easily do a Valor Bard warrior-poet (I actually attempted that on one of my 5e characters), or an Eloquence Bard orator, or a Swords Bard circus performer, or a Lore Bard ventriloquist, or whatever might tickle your fancy.
Paladin Oaths are super easy to recast in new lights, particularly because the tenets described are more like loose guidelines for your own stuff. I preferred the old 4e version of Lay on Hands, but as it is, it's literally just "you have a pool of HP to use." There's nothing saying a Paladin's holy smites have to
look holy, and indeed the Oath of Vengeance works quite well for a Batman-style "dark knight" without actually being
evil in any way.
I would consider Bard and Paladin to be high on
default flavor, but extremely easy to shift to some other flavor if you want. I find classes like Fighter, where the flavor is
completely nonexistent for several subclasses, WAY more difficult to do anything with. If I don't
like the flavor of a class, I can almost certainly change it or at least refactor it in a more useful form.