The banishment movement has the backing of the Kemalist elite and military. In the past, any effort to impose a greater Islamic identity on Turkey was viewed as an attack against Mustafa Kemal Ataturk’s reforms. Turkey has basically been a functioning democracy with the military as the enforcers of democracy in the mold of the cult-like figure of Kemal. The military has done coups in the past against perceived threats.
The court has also outlawed parties before including parties in the mold of the AKP such as the National Order Party, Welfare Party, and the Virtue Party. Plus, most of the judges on the bench (more than needed to outlaw the AKP) were appointed by the Kemalist former president.
The court could very well outlaw the AKP, ban the leaders from politics, and perform a “soft coup.” The military would then make sure a CHP Kemalist administration takes over. This will subside any rising Islamism in Turkey for now but as history has shown it will come back.