You do not have to be a Jew to be a Zionist. If Zionism depended exclusively upon support from the Jewish community, Israel would have never been established.
You do not have to be Atheist to be a Communist. Catholic priests in Latin America, and devout Muslims in Kerala supported the Communist parties in their respective countries.
And no, you do not have to be a Muslim to be an Islamist. You simply have to recognize the logic and wisdom and social good of the policies Islamism advocates. But here is where we run into a problem not faced by other political and economic theories: we have no policies.
If we start to develop policies, instead of simply shouting slogans, we can begin to establish meaningful grassroots support from across the entire spectrum of society. Until then, Islamism is nothing more than a vehicle for ambitious would-be politicians to compete for popularity and possibly for government positions where they will maintain the status quo.