The fact of he matter is that volcanic ash can seriously damage the engines of an airliner.
It's not really an issue that physical damage will occur according to my father-in-law who spent 50 years of his life designing and testing turbine engines at Rolls-Royce. In fact, a lot of the parts you see in today's jet engines probably have inherited some of his designs. (He did a good job and even got an MBE) Anyhow, he explained to me that there is no real issue, especially with today's advancing engine technology. The only issue could be that in very heavy density ash clouds, an engine flame-out could occur. However, in his opinion there is some other reason for the flight restrictions as in general the engines are unaffected. (The ash clouds would have to be much more dense before they became a threat to a jet engine)
Actually yes, the red zone is a no go as advised by the authorities. But in terms of the grey and blue zones it is up to each airline to do it's own risk assessment.