Anyway, Protestantism should remain Protestantism and not Lutheranism; even with Reformed and Anglicanism split off, there are still more flavours of Protestant than Lutheranism. And Anglicanism is DLC exclusive -- in the base game it's still represented by Protestantism.
And likewise, Reformed is not the same as Calvinism -- Arminianism at least is distinctly different.
Actually, we already have a concept in game which is remotely similar: Sunni and Shia have schools of law which give varying bonuses and affect diplomatic relations, without splitting Sunni and Shia into mutually heretic "denominations". Something like that could be done here as well: "Protestant" as a religion (being denomination of Christian) + modifier of Protestant "branch".
I actually really like this idea. It would give the protestants both more flavour and more pwoer relative tot he Catholics.
That's the whole point of Church Aspects. Each countries gets to tailor their version of Protestant to create a unique combo of bonuses.
Those don't affect diplomacy. And honestly, the way it currently works is a bit too abstract and gamey -- they're just buffs you swap around without regard to how the doctrines ought to affect you're country. This obv. isn't important to everyone, but I like roleplaying and immersion, and I fear that the game is starting to sideline that. (Though in this case, the problem of Protestant doctrines has been around, though the fact that the game even more actively incentives you to switch makes it worse.)
And in terms of Anglicanism; I think it either should either have no diplo penalties viz. Protestant, or at least have reduced penalties. I'm pretty sure that Anglicans and Lutherans got along better than Catholics and Orthodox, and the latter have reduced penalties.
If a High Church v. Low Church slider is implemented for Anglicanism, I'd also say it could affect relations with Catholics and Reformed.