Is asking someone if they are a Zionist considered offensive? Is it equivalent to asking someone about their religious or political affiliations?
Zionism is a political ideology, not a religious ideology, whose basic premise is that the Jewish people have the right to self-determination and their own state in the Land of Israel. Within this political ideology, there are devoutly religious Zionists and ardently secular Zionists, and everything in between. There are also devout Jews are are non-Zionist, or anti-Zionist. And, to complete the picture, there are also Christian and Muslim Zionists out there (just surf around a bit...).
So Zionism is a political ideology that an individual may subscribe to, regardless of the person's religion, race, sex, etc. Is it offensive? It depends on the relevant society: if members of a society tend to divulge information about their political beliefs, then no, it is not. It's like asking someone if they're a Marxist, a socialist, an anarchist, and so on.