Many Jews are not Zionists and many non-Jews are. Zionism is a political movement, not a race. To say Zionism is the Jewish people is like saying the Democratic Party is the American people. Jewish people who oppose Zionism, however, have been given a very hard time.
There's more than one mosque in the world that used to be a church and before that was a temple. Because it's a lot easier to just change the sign on the top and say under new management than it is to change the whole building.