When you have so many people talking past each other because they're bucketing groups of people and assigning to them beliefs and behaviors while dismissing concerns with the casual "do all x believe y?" with on-going violent results, I don't think it's pedantry at all.

In less heated times when people are engaged in good-faith debate, we can be more lax with our language. From the discussions of the past few days, that's clearly not the case right now. We're unlikely to get past this without first being more nuanced ourselves.