Necessity is the mother of pragmatism. Islamism makes all sorts of pragmatic bargains with all kinds of secular movements - the far-left, other religious groups, liberals, nationalists etc; and normally there is lip service to the idea that sectarian conflict must be avoided. Heck, I've seen Ahmadi-led groups take charge in some European muslim circles.
Famous members of the Muslim Brotherhood when they were young: Gamal Abdel Nasser, Yasser Arafat.
With the specific Shia-Sunni split, the issue is more that that throughout MENA the split is more intrinsically linked with an ethnoreligious identity, in a way that we wouldn't see in the Christian world anymore outside of NI and the breakup of Yugoslavia.
“Are the Shia population in this country Persian fifth columnists?” - many Arab leaders around the region since 1979, from Saddam Hussein to the al-Saud.