It's so easy to throw stones. To govern an actual representative democracy - wherein belonging to a certain political party should never be a disqualifying factor for political appointment - is not so easy.
I think you would agree that in the past 30 years, the GOP has done exactly that: anyone who was not a line-toeing Republican need not apply, right?
But you seem to suggest we do the same.
The choice is as Anthony Galli said in his reply: in a republic, one must compromise. The GOP devolved to where it is now because they rejected the very notion of compromise (just as Barry Goldwater predicted back in the early 1960's). He warned of the danger of religion in politics. Religion became their means to political power, and now they can't find their way out of the self-made trap.
The means to that dangerous end doesn't need to be religion. Once we begin rejecting people based solely upon their political party (within reason, of course), we face that same danger.
America must be governed as a representative democracy and republic *should* be governed. It's a hard, frustrating path, but it's the only one for a functioning democracy. Otherwise, our democracy is an exercise in futility.
Lastly, here's Goldwater's quote. Yes, he was a Republican, but his quote is spot on:
“Mark my word, if and when these preachers get control of the [Republican] party, and they're sure trying to do so, it's going to be a terrible damn problem. Frankly, these people frighten me. Politics and governing demand compromise. But these Christians believe they are acting in the name of God, so they can't and won't compromise. I know, I've tried to deal with them.”