I don't honestly remember there being such outrage at the appointment of Hodgson. Some of my pals that follow LFC were touting him long before he got the job. I was pleased with the appointment myself tbh be honest. I dare say there were those who weren't pleased but I don't think you can blame them for a manager having such a poor win percentage. I and most others agreed that Rafa had to go.
When AFC appointed Broon there were many who disagreed. He's "too old/negative/shite". I don't blame those fans for Broon's poor results. I blame the unbalanced squad, the down right delusional shite spouted by Broon to anyone who'll listen and the baffling and negative tactics for his poor results.
If you're manager of a football club you have to man the fuck up, show strength and prove the doubters wrong. It's your job to shut them up. If the fans that didn't like him caused such shite results then he's not good enough to be in charge anyway. That's how I see it anyway. Look at Pardew. 99% of folk laughed or were devastated (depending on who they supported) when he was given the Newcastle job. Just about every NUFC fan/follower that I know facepalmed. Pardew went about his job and ended up having a storming season and proving them all wrong and shutting them up in the process. Roy getting the boot was his own fault and the correct decision.