Wanna make it clear I'm not defending Jigsaw. However, Jigsaw has by far the most consistent ideology of everybody shown in this image. Scar, Voldemort, and even Cruella are all simply in power struggles of sorts, and that's their ideology, wanting to be powerful. Jigsaw doesn't need more power in the movies, he's already infinitely more powerful than the people in his traps. But Jigsaw kidnapped a ton of people from a health insurance company for all the deaths they had given other people through austerity. Jigsaw may have an extremely warped moral compass, but he still has a moral compass that is completely separate from being powerful. He wants to punish people who have actually done bad, and I think he'd be pretty pissed over an entire nation of people being genocided.

As a character, separate from my own feelings, Jigsaw is infinitely more likely to side with Hamas.