I said it on another post as well, but Democrats probably do like cops and soldiers as much as the Republicans if not more. Democrats want a truly professionalized settler-colonial apparatus to protect them and their urban PMC/petite bourgeois base from the poor. This necessitates them critiquing policing as it exists however. They dislike that any racist shithead with a highschool diploma can join the force and gun down people in the streets because it makes the racial and class nature of the state very clear. Democrats want cops who are trained for four to six years in how to be a polite colonial enforcer. Democrats want cops to more like USAID and less like the marines.

Republicans retain a frontier culture and mindset, which means they empathize with cops brutalizing black people because that's what they want to do. At the same time some recognize the repressive force of the police and actively dislike them. Regardless, the only frame of reference they could criticize police from is from their imagined position in the frontier which is as amateur settler-colonists oppressing non-whites. This is the same affect many police have so Republicans reject any criticism of the police.