Political Memes

That adage is pretty much the opposite of true. Republicans make demands of their politicians, and have no reservations about loudly denouncing them as "RINOs" if they don't follow through. The biggest third party candidate in history was Ross Perot in '96, because Republican Bob Dole was seen as too moderate and mainstream. Part of the reason that the party establishment didn't stop Trump from getting the nomination was because they knew there was a credible threat that he'd run third party, while the Democratic establishment resisted Sanders, because they knew he'd fall in line anyway.

The reason the adage exists is, ironically, because democrats are more prone to shaming voters who step out of line. From what I've seen, in right-wing circles, complaining about RINOs and shitting on the Republican establishment will get much less pushback compared to the opposite. Those who try to lecture and vote-shame are more likely to lose credibility themselves than the person they're criticizing.

Of course, because the party has received the message and fallen in line, there's less internal dissent, which is used to push the message that "Republican [voters] fall in line," used to pressure Democratic voters to fall in line.