Which is dumb, but the obvious thing to do is campaign to block the massively polluting power plant part of it, not the building with computers in it. As the GP said, these companies have insane market caps, they can afford to build renewable power.
It feels like at some point our society forgot that the government is supposed to pass laws, and not just block things we don't like. Data centers are being built with polluting power sources, why is the instinct "stop all the data centers" and not simply, you know, require them to not use polluting power sources?
Also, while I'm glad you're focused on what matters, 90% of the outcry I've heard about DCs is about water. Or noise pollution, or them looking ugly... for buildings that, again, are mostly being built on razed industrial land or empty fields. According to the OP, "electrical grid" is the fifth most common concern, and air pollution is wayy down the list.