Check out RAWK.
For every damn Rafa out thread, I'll find you dozens of Rafa's appreciation threads there or in any LFC forum.
Some people did want Rafa out, but were deluded enough to think him to be replace by Mourinho or Hiddink or someone of that ilk. Thankfully they were among the minority.
Roy was not really wanted by anyone, he was just a fallback/safe option whom fans thought would do well, AFTER the sacking of Rafa. Most people preferred Pellegrini at that time.
While Liverpool fans do often change opinions as quick as anyone else, see Purslow and Broughton, but Rafa, Roy is not a good example by any means.