There is no number of foreigners that is unacceptable to sacrifice for a middle class livelihood. Anti-cop because they can imagine a scenario where a cop inconveniences them. These principles don't apply to the Waffen SS because they can't imagine a soldier personally inconveniencing them and, of course, foreigners aren't really humans.
I’d argue that the military propaganda is more effective than the copaganda, even though you’re right that there’s more copaganda. But I think your reasoning is the answer to that too: Copaganda isn’t as effective because it’s disproven every time you actually have to interact with a cop in real life. But since Americans don’t get harassed (or murdered) by soldiers like they do by cops, the reputation of soldiers doesn’t fall in the same way.