I am going to Içmeler next week and I am worried about all this trouble just now. Is it safe to go just now?
For Turkey, Iraq and Syria borders are places for possible safety issues, But for Touristic vacations, you probably never go the border.
For south eastern towns are rarely have problems about terrorist activities but since the clashes with the army is always on the high mountains you probably will not have any problem about visiting touristic places like Mount Nemrut in Adıyaman or Mardin. You can consult your travel agencies for more and better information about the tourism in these parts of Turkey.
Beyond that, it is all safe. Anti-government protests do not take place in touristic places. Istanbul Taksim Square is the only exception but there are no big clashes for a long time. With watching the local news about Taksim, you may have safe visits in there too. Beside Taksim, rest is totally safe.
Elsewhere I replied this:
The general answer is yes. It is safe to travel there. Nevertheless, Turkey being a very big country one cannot lump everything together. The more detailed answer to this questions largely depends on where you go.
Now your question is more specific. And the answer is definitely yes. Içmeler is safe. It is definitely far enough from the more agitated regions in the Southeast.
You should also know that there can be some street crime, i.e. pickpockets and alike, especially in the more touristic areas. But that's the case in many many other places. Nothing to be especially worried about, especially in comparison with other destinations.