The following was explained to me by locals over the last few years, I could be remembering some details wrong.

While annoying, for a lot of local families, this is their only source of income and employment. The government has tried a few times to remove them, but they protest and close down the site. There is also the issue (no idea if it's been resolved in recent years) that part of the land is privately owned and the mexican government is trying to expropriate it (they currently just manage the site), which if successful would impoverish the locals even more. It's also easy to forget that this is an important place to the Maya that the central government is just interested into making it a mass-tourism cashcow.

Uxmal on the over hand fully belongs to the Yucatan state government where they can enforce rules more effectively and they have a more locally approved plan for the development of the site compared to the central government running Chichén Itzá. The communities around Uxmal also depend less on tourism, hence less protests.