Comment by harimau777

I think that there's potentially a couple of things at play here:

Taken literally, the idea of a "thin blue line" protecting society from chaos has some authoritarian overtones.

It's a slogan that tends to be used to simply dismiss problems like police brutality. That is to say, it comes across less like a difference in policy position and more like indifference to the suffering of others.

The political faction that it's associated with, i.e. MAGA, is currently in the process of attempting to purge anyone with a worldview that they dislike from public society.

All of those factors creates a situation where it is difficult for those who use signifiers like "thin blue line" to practically operate simply as "people who happen to be conservative" as opposed to "people who represent an irreconcilable threat to people they disagree with".