I don't have the scientific or engineering background to understand the physical damage such atmospheric condition may (or may not) cause a jet engine. But, I certainly understand economics. And, even if it's dangerous - perhaps even dangerous enough to cause a catastrophic engine(s) failure - that economic uncertainty is FAR outweighed by the economic reality of the ban.
Simply put, those airlines could probably lose a jet a week, and still be ahead (financially) where they are with the ban in place. Given that economic and financial reality, I'm not sure I'd place too much faith in what the airlines say.
What about the Finnish reports of F-16s requiring complete engine overhauls after having flown through these clouds? I’m sure someone can put up the pictures here.