The obvious answer to the question is "everyone that lives here does"...
For most people Christmas is more of an event than a religious thing meaning that it is - but of course in its own way - celebrated by everyone even in a Muslim country like Turkey.
Also no shop in Turkey is blind to the commercial aspect of Christmas so currently all shopping is accompanied by Christmas decorations and jingle bells.
Some even claim that Santa actually comes from Turkey and not the North pole, Finland, Greenland or anywhere else.
With that said celebrating Christmas in Alanya is of course very different than celebrating it at home. The special Christmas mood that you find in your home country can not be replicated anywhere, no matter how hard you try.
People who choose to travel to Alanya during the holidays do so because they want to get away from all the Christmas activities at home, so they surely do not mind.
And all of us living permanently here in Alanya do not have same expectations to Christmas as we would normally have.
Instead we make Christmas our own way and try to mix some of the traditions we know from home with the opportunities that are available in Alanya.