The internal factions and politics in that part of the world a not easy to understand from little snippets you read on the internet.
And the "people" don't always support things that a western person would agree with. People always assume that if there is a popular revolt it would always be in the direction of democracy and secularism - it's not so at all.
Don't support a popular revolt just because it's by the populace. Support it if you think it's right. And if you don't understand the situation then reserve judgment.
Syria/Assad is one of the biggest fascist/dictator. He can't give democracy lecture to Turkey. He does not have a right even comment about Turkey democracy.
Turkey people haven't support Assad or the groups against to him. Turkey folks always supported helping to syrian refugee, thats all. As folk wanted, Turkey government helping the syrian refugee while supported the groups againist to Assad. The supporting groups goverment's initiative.
The problem of the Turkey is between folk and government. Its not unfixable, we'd like to government's support even small groups like gay's, homeless people, women rights. We don't want despot behaviours form cops to folk. Basicly the protests are about small problems, to be have better democracy, as well as better even some part of europe/usa.
It is not that the protesters support Assad it is that they don't think they should be getting involved in the conflict. They view Erdogan as wanting to create a modern Caliphate and with the power they already have, that getting involved in the Syrian conflict is the next step at expanding its influence.
Wait, I thought Syria/Assad is the bad guy. The Turkish people support Assad but the Turkish government doesn't? Now I'm confused.