I don't agree that demonising the entire religion serves to demonise all those within it, and the claim that it does is used almost exclusively by people who have bad motives and want to shut down debate. In the Cold War, this was called 'semantic infiltration' and is a tactic used to control the parameters of debate through the control of language. In the case of Islamists, this tactic is seen in the reframing of the utterly meaningless word 'Islamopobia' to make it impossible for people to criticise Islam without being called a bigot.
If you're worried about a rise in anti-Muslim bigotry (of which there is of course plenty), then the best thing you could do to tackle this IS demonise the religion. Because it is the perpetual, almost pathalogical, reluctance to say that these problems are rooted in Islamic scripture that is doing more than anything to make people less inclined to differentiate between good and bad muslims and just lump them all in together.