When you say they subverted the initial protest, do you mean before or after the police clamped it? I'm just wondering because if they'd politicised (to some extent made more extreme too), that could explain a lot about the police action. Alternatively, maybe the police made a bad shout upsetting a peaceful protest and these parties capitalised on angry people?
It's inaccurate that the protests are subverted by these 3 political parties. This may be a pro-government or right-wing argument and it lacks the understanding of the true nature and motivation of the protests.
This was the turning point of everything and people wanted to go to Gezi Park to support protesters. The governors response was escalating the police power and excessive use of tear gas. So the protests evolved to a anti-fascist and anti-government movement.
PM Erdogan's response to the protests was nothing but provocative. He insisted that they have made their final decision for the park and they will not retreat. He also announced he will build a Mosque near Gezi Park (an extremely controversial project that has a former history) and they will also demolish Ataturk Cultural Center (an opera/theatre house across Gezi Park, having a symbolic significance representing the secular values of Turkey and carrying the name of the founder of the modern Turkey). He likes to call such projects as "crazy projects".
Erdogan's provocative attitude was nothing new. In a typical week in Turkey you hear more controversial things from him. But for about few months it's getting worse and worse, and more authoritarian and conservative. Erdogan's Syria policy and last terrorist attracts was one of the reasons of discontent. The opposition parties were inadequate and there was blackout in the mainstream media. So people waited without any reaction for long time. This Gezi Park "crazy project" was just the last straw and everything escalated so quickly.
Your comment is pretty much a much better written version of the story I knew so far. The comment I replied to seemed to suggest something a bit different, with a coalition of political opposition taking advantage here. I wanted to see where what I knew fitted into that narrative so I could try to form an opinion on it.