The Problem with Paladin Villains (spoilers for SoD/GDGU)

[Worldsong]

Whether paladin A can exist or not in DnD rules somewhat depends on how one interprets the rules. A DM or writer could create a scenario in which a Lawful Good deity is trying to create an army of Good to fight against Evil and to that end is telling their followers, most of which being paladins, to create an empire of Good where worship of said deity is mandatory (to ensure more soldiers for their army of Good) and all laws have to be strictly followed with draconian punishments for those who fail to do so to prevent Evil and Chaos corrupting the empire.

One person could say that this empire is actually Lawful Neutral because it's basically a system for churning out fodder for the war machine, but another could say that a Lawful Good empire doesn't require freedom of religion and that the rules are harsh but fair, with the soldiers being devoted to a Good cause (namely, the elimination of Evil).

EDIT:
And yes, such an empire could then make frivolous activities such as singing and dancing illegal and require the people living there to spend most of their time working and praying for the sake of strengthening the empire and spreading the faith. The fight against Evil requires devotion and dedication, after all.