> What if they see that group as a legitimate target for political reasons?
It doesn't matter. I wouldn't engage with whether or not they think they're acting in a justified manner. If the behavior won't stop, the behavior is harmful, and the community would be better off without it, then sometimes you just have to kick someone out.
The reason why I say politics are a distraction is because I don't think you need to bother to explain that someone is politically incorrect or how you are less so. You can, but none of that is actually relevant in a majority of cases. Removing someone from a community is not about being more correct or about them being incorrect, it's for the good of the community (and/or the good of whoever you're removing).