My electricity bill is 50% higher than this same month 1 year ago. My friends and neighbors in my city have said that they also have greatly increased electricity bills. Whether or not that increase is due to a specific data center, it's extremely easy to blame it on the increased electricity usage of data centers, no foreign propaganda required.
If the problem is demand outstripping supply then the obvious thing to insist on is that if they want to build, they should add more supply than they're consuming, so that they're fronting the money to make your electric bills go down.
Whereas instead we keep seeing proposals to ban them outright, which is the thing you'd expect to be pushed by someone with a different interest than domestic electric bills.
My electricity cost per kWh has just about doubled over the last 3 years, but afaik, it's mostly related to legislated changes to the energy mix and increases in fuel costs.
Fuel costs are up for lots of reasons, more demand for electricity could certainly be one of them... Inflation is certainly another component.