Because the average person doesn't know the direct ties between Christianity and Nazism, so it's a good tool to catch them up to speed.

I mean…you kinda said it there. European fascism can trace its lineage to European Christian kings, empires, and popes. But that’s fascism born of Europe. As others have said fascism has been and is practiced elsewhere and with different religious and cultural influences.

Christo is merely an aesthetic modifier. It tells you what surface level flavor of fascism to expect. Remember that Nazis used language and themes of socialism in their aesthetic as well. It’s why we still refer to them as Nazis and not solely fascists.

Though I understand your point. Why not call a christo-fascist and a Nazi the same thing. You certainly can; no one’s going to stop you. At its core fascism is always the same malignant stage of capitalistic rot. It’s practitioners will use whatever aesthetics they wants. Whatever works. Some may find it useful to describe the aesthetic quality of one fascism to expose its core similarities to other instances of fascism.