Jigo lays a trap that sacrifices hundreds of his own men in order to kill a god.
I'd put both of them in the villain category. Before the battle, I wouldn't put either of them in that category, but the climax really makes them out to be awful people. Eboshi in particular hides behind smiles and buying up the contracts of prostitutes (to make them her slaves) and helping lepers until the climax when she completely abandons them, throwing them to the wolves in service of money.
She is absolutely a non-evil, non-villainous antagonist.
Eboshi is socialism. She cares for the people in her village and will overthrow gods and warlords to protect them. She’s in direct conflict with the forest gods and has what she thinks is an opportunity to bring peace. She’s willing to put herself in jeopardy for her people. I have never assumed anything but her pure altruism for the people of her village. She’s the type of leader you want to protect you and don’t want to be up against. That protection doesn’t exist in a vacuum, and just like historically socialist societies, she’ll use violence to achieve what she sees as ideal.
Jigo is capitalism; self centered and money motivated. He’s just a bounty hunting mercenary. He doesn’t care about the consequences, just about getting his job done. He does have some loyalties and is very honest about his approach to the world. The men he eliminates are not his men, but local samurai who are the least morally ambiguous. He’s not a hero trying to protect Irontown from the same samurai, but at the same time, he needs to ensure he comes out with the prize, otherwise he doesn’t get paid. He’s calculated and efficient, and his men actually kill two birds with one stone.
It is the emperor that wants immortality and triggers the chain of events that get the main forest god killed & cause a lot of destruction. And in the end - he is still unaffected, while Eboshi & co have to rebuild all of their infrastructure almost from zero... :P
That’s the joy in most Miyazaki movies. Any other movie would have an obvious evil villain. Miyazaki gives all of his characters motivation that is immediately relatable. Sometimes characters that appear to be villains at the beginning are heroes at the end.
All of these things mirror the real world. Rarely is someone actually intentionally evil. They may have different priorities, goals, fears, and motivations, and those may produce behaviors or beliefs that seem bad, but without understanding the why or what, it’s easy to just assume their “bad” people. Ashitaka doesn’t take the bait and is kind, respectful, and generous to everyone who isn’t obviously doing something atrocious (like the samurai slaughtering peasants).
Princess Mononoke is easily one of my favorite movies of all time and my favorite Miyazaki movie.