I'm not convinced that "showing empathy" is the way to court Republicans. It's just seen as weakness, and weakness is a joke to them.
I'm thinking back to my grandmother's funeral in Appalachia. She had a small terrier as her companion in her final years. They were inseparable. Multiple of her male relatives made the joke "I thought we were just going to toss the dog in the grave and bury him with her". Hardy-har har. The dog was small and therefore weak and therefore a joke.
There were similar scenes between my mom and her coworkers when my dad was in hospital dieing of COVID-19. I'm not going into them because I already done triggered myself.
Anyways, that's how I ended up with a surprise dog to take back home to a blue state. He's still a good boy, even though he's now a grumpy teenager.