If it's true that the Military is trying to keep the government and religion separate, how could you not root for them?
Church and State are separate
Erdogan was prime minister for 12 years. The AKP liberalized and democratized Turkey over the last decade and a half. Remember, Turkey tried to join the EU and the AKP was able to make the argument that the military coup culture had to be eliminated and power restored to civil society. They succeeded in that for the most part.
The last couple years you've seen Erdogan attempt to power grab, he became President which is a ceremonial post and had tried to gain a majority in parliament to change the constitution and make it a presidential republic. He's jailed journalists, suppressed dissent and gone after opposition groups.
He's attacked Kurds but to be honest, every Turkish party hates the Kurds.
The bad news for him is that there are some in his own party that don't want that.
Turkey has checks and balances, Erdogan hasn't been able to get everything he wants.
This isn't about Islamist vs secularist like CNN and others want you to believe. Turkey is a Muslim country with a secular government. It's ruled by a Muslim party that has been able to transform the country. And they are still immensely popular for that reason.