I think right wing politics being "law and order" is more just virtue signaling. A way to feel superior, morally justified over left wingers, despite the fact that the vast majority of left winger and right wingers, would agree to the vast majority of the same morals.
I think reducing conservative support for "law and order" to virtue signaling is simplifying an interesting issue a bit too much. I personally feel like a lot of it comes down to the heart of Conservatism: the preservation of traditional institutions and the status quo. The police are largely seen as a means of preserving that status quo. That is why a lot of Conservatives (particularly Conservatives who have traditionally benefited from police bias and the systems they protect) will say they support the police with their full chest, but then lash out and attack them when they see them as betraying that goal (See the Conservative response to the Capital Police after 1/6).
Conservative support for the police is not just support for the police, it is support for societal tradition, and as such, that support is contingent upon institutional support of those systems.