This is a leading question, if not leading
and double-barreled, but at least you provided an option for me that allowed me to answer it.
I believe a player should be able to play monk or assassin in any campaign, even if it is medieval-Europe centri/tolkien based/etc, ON THE BASIS that they have a good back story explaining why they are of such a vocation. Perhaps the monk was banished from his lands, and now must travel without a home to regain his piety?
The "assassin issue" is murkier water yet. It is hard in many campaigns to distinguish good from evil, because the alignment system falls victim to a whole lot of relativity and subjectivism. As a PC (yes, PC, not player) put it in one of my "evil" campaigns:
"I'm fuzzy on this whole 'good' and 'evil' things. I believe what I am doing is the best thing to be doing, but you are clearly in opposition to what I strive to achieve. I am therefore to say that you are the evil one, and of course you take me as the villian. Who is more right? Perhaps none of us are."
Is a hired blade
always doing something evil? It depends on your standpoint. If killing another human is
always an evil act, there are many paladins that ought to lose their powers, and most adventurers are evil. So Assassins should have a good back story too. Why did they become assassins? why are they still in the profession? those are the kinds of things that sepearte the malignant adventurers from the vigilantes.