It will effect dialogue. Every class has tags associated with it that impact dialogue options. So hypothetical barbarian Gale would lose his [Wizard] dialogue options, keep his [Gale] dialogue options, and gain [Barbarian] dialogue options.
Of course this will only be seen if cutscenes/dialogues are initiated with them so it's somewhat avoidable if you aren't playing as them.
But the fact that Gale can become a Barbarian and lose spellcasting entirely, but like he'll still be casting spells and so on in cutscenes and his abrupt and dramatic change in profession is never addressed is pretty jarring IMO.
