It was a scum bag move and he proved himself to be a scum bag. On that point the fan base should be happy that they're rid of him, not angry that he left them.
As far as his securing his next job before the season was over, it wasn't the first time someone pulled that and it won't be the last. When it happened at Michigan 35 years ago Bo Schembechler fired Bill Frieder and his replacement won the tournament. If Cooley putting his house on the market was so offensive, PC should have done what Michigan did when faced with the same situation.
What I believe warrants criticism is the PC fan base is behaving like this is something that has never happened before and that they've been wounded at a level beyond anything anybody has ever seen. They are overreacting at a massive level (producing the documentary, referring to him as Hitler). He left, get over it.