For either to happen, Turkey would almost certainly have to become an Islamic country. It is mostly Islamic, but politically secular. As pointed out in the above blog, that appears to be changing and many people don't like it. That's part of the reason there is so much rioting going on there now.
However, President Erdogan has very little patience for these rioters and if he can't restore order soon, he is liable to declare something akin to martial law. He has his own people in place in the military so the threat of a military coup, which has happened several times in the past, is very limited.
With martial law, Erdogan can instil more Islamic values on the people in the name of peace and good government, thus taking them one more step closer to a full-out Islamic state which would, most certainly, be an enemy of Israel.