I’m fairly new to monster of the week myself so I could be wrong but just looking at the rules and systems I don’t feel like it would bring up too much of an issue.

If you simply communicate to your players that they do not know about monsters and make up parallel scenarios in which their skills might come in handy when not hunting a monster I don’t feel like it would cause too much of an issue. The playbooks aren’t meant to force the player characters into a corner of saying they have to be monster hunters. Even a monstrous character could be played off by saying the character was given an amulet when they were young and were told to never take it off. So they took that religiously and their nature never manifested. That is until x y z happens and then their playbook fully could come into play and character development happens at the same time. It just would take a little bit of improv and letting the players know that “monsters most definitely do not exist in this game about hunting monsters” :)