Why not? Doesn't media regularly customize their headlines to avoid stating factually true things that would propagate negative stereotypes against minorities and other protected groups?
I think most responsible media organizations do avoid putting headlines like "Muslim man stabs three in church in Nice". Even if they do mention the religion, it is usually called "Islamic terrorism", and they have also invested quite some significant effort into emphasizing that most of regular Islamic people do not in fact have anything to do with Islamic terrorism.
As far as I can tell, media companies certainly seem to be aware of the effect their headlines can have on propagating negative stereotypes and good editorial judgement usually involves an attempt to avoid doing that as much as possible.