But whenever we do say that those evil people aren’t Christians and push them away, we get accused of “no true Scotsman fallacy” or some BS and “you are part of the problem not taking responsibility”.

As for coming up with a new label, the thing with the label “Christian” is that it’s prescribed in the Bible. Even other religions far removed from Nicene Christianity that respect the Bible or some form of it use the label, such as Jehovah’s Witnesses and Mormons. So the productive thing to do is calling them out on not being one for not following the teachings of the Bible