Do I use the character class rules to make NPCs? Yes.
Do I refer to those NPCs as Fighters, Clerics, etc.? No.
I voted No.
That being said, one thing I really enjoy is thinking of things from a commoner's perspective; average folks don't know the fine details of anyone's profession any more than I know what really separates a project accountant from an investment accountant from a CPA. A person who casts spells is known as a sorcerer or a warlock and is terrifying to the common person, whether that spellcaster styles themself a wizard, cleric, bard, or whatever.
So the players never know exactly what to expect when they are obtaining information from the locals.