Paladins are religious fanatics.There is a war going on between the opposing forces of Law and Chaos. Sometimes it's a cold war, sometimes it's hot, but it never, ever ends. The various divine powers are ranged along either side, with a few remaining more or less neutral. There are allies to be dominated or appeased, there are fence-sitters who might be swayed either way depending on their own interests and there are enemies to be obliterated. And the battlefields are, of course, the various inhabited planes of existence, of which one is the home of Our Heroes.
As in any war, most soldiers are just trying to make it through, and with a bit of luck, get their buddies through too. They may think their opponents are kind of dicks, but they don't dwell on it. They may even get along quite well with individuals from the other side, depending on circumstance. The war is just background noise, except when it gets up close and you have to scramble to get through with a whole skin.
Paladins are a different matter entirely. If a paladin comes upon a group who are worshipping, or even just supplicating, one of their own personal deity's enemies, they take it personally. They do not tolerate, they do not come to accommodations, they just GO TO WAR.
I don't mean by that that they're necessarily mindless berserks, foaming at the mouth and going into a homicidal frenzy at the very sight of a shrine to Floaty Bobbles, Lord of the Rubber Ducks. That might be the case, but not always. Many paladins are intelligent and calculating in their never-ending quest for the utter annihilation of all enemies of their god, everywhere.
The key thing is that they're always at war. They're obsessive.
You may have noticed that I've said nothing about goodness or evilness, and that's on purpose. Those traits are irrelevant to the war as a whole. They will certainly affect the way a given paladin approaches the problem of destroying the cult and shrine of Floaty Bobbles and punishing those who have collaborated with the Bobblites, and certainly a good paladin is less likely to entertain the idea of Acceptable Collateral Damage than is an evil one, but each is just as obsessively driven as the other to the final aim — the utter defeat. and destruction of their enemies, wherever they may be.