Remah lived when Protestantism was just emerging, so we may want to look at later poskim also. One possible hiluk may be that it is avoda zara for Jews, but not for non-Jews. A book by two experts says so, but when I asked the first author, he said this was only because his co-author insisted so much, so I don’t know whether this is a strong shitah.
Islam was not considered avodah zorah in some of the times when they were even crazier than now, what changed now? Who said that only idolworshippers can be crazy?