Not exactly. Much of the anti-datacenter population got that way from hearing about the irresponsible ones and don't want it happening in their area. If they never heard about it because it was in the middle of nowhere, then they wouldn't be involved. It's NIMBY - data center or houses, don't build it near me.
A datacenter has way more impact on it’s surroundings than housing, I don’t think it’s fair to say they are both coming from the same NIMBY sentiment. Anti-housing NIMBY are afraid to see their overvalued houses reduce in price, while anti-datacenter folks see how loud and damaging they can be and say no