Kasha,
You confuse two issues: Whether another religion constitutes idolatry, and who is permitted to practice it.
You have continued your practice of cherrypicking your favorite opinion who argues against the overwhelming majority. This is not the way to discuss halachah, at least if one is Orthodox. Rambam clearly said that Islam is not idolatry and criticized those who said that it was. Furthermore the Ran’s statement that Muslims bow down to Mohammed is flat out false. I’m not aware of any important poskim who have agreed with the Tzitz Eliezer on the mosque issue. (If you know any, please cite!) The Tzitz Eliezer is certainly someone who can be followed — and indeed in most areas of medical halachah he is followed in Eretz Yisrael — but don’t criticize those whose rabbis rely on the majority.