I feel that the resentment to be short sighted. Datacenters do not vote, but people do. If a datacenter is in a locale, it gives those voters a de-facto, outsized, soft power.
No, it doesn't. Voters decide very little in the United States. People with money decide almost everything. They have better lawyers and better lobbyists than you do.
If you go in with the assumption that democracy does not work, then there is also no point in protesting, as being angry about datacenters would mean nothing anyway.
You, via your electeds, (in theory) have more power over a datacenter in your own jurisdiction than not. Though that does depend a lot on your electeds not being in the pocket of the datacenter's owners, and on the regulatory environment of the country/state leaving power available to city/county officials to do anything.