::::::True, but the main point seems to be that there is a lack of any real evidence. There isn't even good evidence (on the internet) of rumours! I guess the whole thing has grown out of sectarianism in Liverpool city, of which there was some. On a small scale there probably was a sectarianism between clubs, but it was as likely to be one way around as the other. Then this weird urban myth sprung up from somewhere.  
 ::::::Looking at the fan-written evidence it would seem that there is some claim for Everton being "the Catholic club". I can see a way to integrate a sentence or two about Everton, having in the past, been considered, by some, as "the Catholic club", into the Everton article. However it's hard to formulate a good way of saying that Liverpool FC, during the days of sectarianism in Liverpool, were considered, by some (Everton fans), to be "the Protestant team".  
 ::::::The oddest thing is that Everton seemingly have the stronger ties with Rangers (i.e. Catholics befriending Protestants) and the perceived wisdom is that Celtic and Liverpool have a history of friendliness. If nothing else dispells this myth then that should.