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
Well a magic infused instrument wouldnt be a stronghold type quest would it, larian would just have you roll to check if you can use it or not, so either you missed the point in what a class base quests is (what i was talking about in the OP) or you are making a strawman.
Secondly if for example you are a "evil" paladin and go do the paladin strong hold quest whats to stop you killing the paladins instead? Whats to stop larian from giving you a quest line to corrupt the paladins.
if you dont like how the quest is working react in a way you think your characters should and see what happens.
And finally it wouldnt be a non class person refusing work as you said
In bg2 if u wernt a warrior you wernt given an opportunity to run the keep
If you were not a druid you couldnt take over the grove
If you were not a thief you where not given the chance to run the thieves guild
Its like having mini secrets in game that add replayability, the i wonder how my warlock would react to those cultits, could my priest of the same diety run that temple?
Can my paladin take over that order?
Lets play again and see how the world is diffrent for a diffrent class