Nearly every religious minority in Syria supported Al-Assad in the beginning. They felt that he did well protecting minorities. They didn’t fear just any sunni leadership, but one that wouldn’t be kind to minorities (and unfortunately some sunni groups made their dislike of religious minorities clear, which enhanced this fear).
The fear of extremist groups taking power has largely subsided nowadays. I think this encouraged the Druze to protest the suffocating conditions in Syria, without fearing that it would lead to extremists taking over.