Perhaps not allowing them to choose whichever class they want, but I do see that there could well be some class flexibility.
Shadowheart Classes: She worships Shar. There can be devout followers of Shar who aren't Clerics. I could see her being a Blackguard, or even a Rogue.
Wyll Classes: Recall, he *was* a Warlock, but he's trying to sever his bond with the patroness. He could be a Sorcerer or a Wizard easily enough, trying to regain his power apart from his patron.
Gale Classes: He certainly used to be a Wizard. However, he was/is a devotee of Mystra. He could be a Cleric of Mystra, or even a Paladin of Mystra, or perhaps a Sorcerer (wild magic, perhaps?).
Astarion Classes: He could well be anything, for all I know.
Lae'zel Classes: She is a Fighter, but she could also be a Monk? I suppose she could be a caster, as well, the way she worships Vlaakith, she could be a Cleric.
All in all, I see each of them have at least three different options.