Many women have been shot by gangs that belong directly to Kadyrov.

As information coming from Chechnya reports, gangs attack those women that do not wear scarfs.

Besides bombardments gangs use the propaganda-leaflets calling girls to carry scarf or otherwise it will be disastrous for them. 

Definitely, some Chechens will support such decision which will "force" women to wear according to Chechen tradition. But it's important to notice that even at the times of Aslan Maskhadov and Djokhar Dudaev, Chechen women were always asked nicely to follow their tradition, because in Islam, nobody has the right to torture civilians for your own decision.

ChechenCenter.info