Do we know that the Kemalist sections of the military participated in the coup? I have not read anything about it. These would be the only ones who would care enough to follow the "protect secularism against islamists" protocol. If the initiators were, as being reported, related to the Gülen movement, then they are religious nuts as well, and what they cared about was simply to bring Gülen in power.

Related: These tweets by Turkish journalist https://twitter.com/ikoker/status/755104366235901952