By any metric, Tayyip's leadership is not secular.
However, the turkish people (at least according to my friends) are are badly shaken after the two recent terrorist attacks - the coup represents more violence - regardless of its 'benevolance'.
Turkey's admiration of Atatürk, the 'founding father' of modern Turkey is absolute: a benevolant dictator, he molded Turkey into a modern balanced country, uniting multiple social, ethnical and religous systems.
It is widely held that Tayyip is doing exactly the opposite: peice by peice dismantling the social balance and fundamentals of Turkey. Naturally, his actions are liked by some - but his goal is to divide, as opposed to unite.
Based upon this, the coup seems to be yet another tangile proof of the disquiet that has been installed under the Tayyip regieme.
Essentially, the turkish people have had enough of bloodshed, division and disharmony.