The biggest strength of the Republicans is also their major weakness - the lack of integrity of the large part of their party base. It's pretty simple: Republicans are disproportionately bad people, liars, morons, idiots. Therefore, their truest candidates are usually bad people (Nixon, Reagan, Bush, Trump). Eisenhower, easily the most decent Republican president since the parties switched, was a bizarre fluke. So they aspire to base emotions - hate, envy, fear, ignorance.
This sometimes bites them in the ass.