"Immigrants have a higher rate of violent criminal activity than Citizens is an ideological purity test for Republicans."
Unfortunately, it's your own myopic, incorrect logic that is making that point. For Republicans, the idea is that if those illegals (remember, Reps are against illegals, not immigrants like you keep trying to incorrectly elude to) weren't here in the first place, the violent crimes wouldn't be committed. So, let's say Americans commit a random number of violent crime, like 10%. Then, you add in just 1% from illegals, that makes it 11%.
So, in a Rep's mind, whether you agree or not, the thinking is that the 1% wouldn't even exist if the illegals weren't here. There is no purity test or random, made-up litmus you try to put into the conversation just because of partisan hate and no real logic or anything. It's the simple fact that if illegal A, who committed rape and then killed a girl, weren't here...that crime never would have happened.
In essence, all liberals are doing is trivializing these violent crimes done by illegals. In fact, liberals fight waaaaaaaay more for the innocent person who may be arrested incorrectly than they do for getting rid of the illegal who committed rape, murder, etc. And this isn't even debatable, it's ALL OVER the media in every outlet, not just partisan outlets.
So, as usual with people who are blinded by partisan hate that they can't understand bad logic, you are making up an argument and then debating it yourself instead of actually listening to the other side, understanding where they are coming from, and then forming logical conclusions. In the 1990s, this was a huge problem with Reps. The pendulum has shifted very far to the left now.