I live in a rural area in a red state and it's quite the opposite. People are perhaps maybe a bit too apologetic. I think the unwillingness to apologize or acknowledge oneself as wrong is a symptom of emotional immaturity rather than political persuasion.

It is more contextual than a simple binary, especially the emotional context. If the event triggers their shame more than their identity, you get the larger than required apologies. If their identity is the primary thing that is triggered, they will get defensive and double down. It's not just a rural thing.

It can be both. Never admitting fault is very much core to MAGA but it's somewhat neutral with other major political ideologies. Being emotionally immature may also make people remorse-averse.