Personaly im not a fan of class based quests at all ...
For one, it gives my class identity that dont necesarily goes works well with my character ...
This is especialy true for classes that are most stereotypical ... like Paladin, Druid, Fighter or Rogue ...
And for two, i dont really see any reason why non-class person would be refused for that work ...
I mean yeah, you probably dont let Berserker Barbarian handle your superfragile magic-infused instrument ... but who would that quest be for? Wizard? Sorcerer? Warlock? Bard? Arcane Trickster? Eldrich knight? And whoever you pick, why exactly would you exclude the rest, do you really want to get the job done, since you are this picky?

Nah ...
I think Larian picked good way to handle this, quests are for everyone, but certain classes can bypass certain dialogue roll, bcs its simply their field of expertise. :3