The group Antikapitalist Muslims has issued an invitation for Namaz in Gezi Park today - they call it "resistance friday" (Direniş Cuması). http://t24.com.tr/haber/gezi-parkinda-cuma-namazina-davet-seccadeni-kap-gel/231468
Yesterday the Lailat al-Mi'raj was celebrated in Gezi: the Park was collectively declared an alcohol free zone for a few hours and a group of people brought and distributed traditional pastries for this holiday. http://www.radikal.com.tr/turkiye/gezi_parkinda_kandilli_eylem-1136463
These examples should show clearly enough that rumours about attacks on muslims and openly anti-muslim attitude by the majority of protesters are simply lies.