There's a funny term that the beltway media still uses in 2015 and it's called a "moderate Republican." The Republican party has changed many times in the course of its history, but ever since the religious right hijacked it after Reagan took office, they've continued on an extremist trajectory. That pace was hastened once Tea Party members was allowed to enter their ranks and the downward spiral of extremism fell off the eastern coast.
Sure, in today's GOP, there are a few politicians that don't adhere completely to their entire xenophobic, free market, warmongering, anti-abortion orthodoxy, but for the most part they still bow down to extremist dogma.
Jeb Bush understands the need for the Latino vote and that's why he's in favor of immigration reform, but when asked about the minimum wage he fell right back into free market claptrap
“We need to leave it to the private sector,” he responded. “I think state minimum wages are fine. The federal government shouldn’t be doing this.” He went on, “The federal government doing this will make it harder and harder for the first rung of the ladder to be reached, particularly for young people, particularly for people that have less education.”
When Sen. Marco Rubio, a one time rising start in the GOP took up comprehensive immigration reform, he was quickly vilified by the tea party until he changed his stance completely.
Senator Rand Paul reflects his father's beliefs against typical US neocon foreign policy, but on almost everything else he falls right in line with a man who wants an unborn fetus to have the right to vote.
Here's my definition of a moderate Republican in today's world.
Members of the Republican Party that frown on shutting down the federal government over the debt ceiling.
You can tweak that formula slightly, but that's pretty much it.
The Republican party has been heading down the tunnel to becoming a far right religious paramilitary extremist group for some time, but when their grand poobahs were frightened by Obama's oratory skills in the 2008 election, they let out the lunatic fringe and now the lunatics run the asylum.
Here's an example of how inane Republicans are today: Glenn Beck, a man partially responsible for the far, far, far right direction of the GOP says he's "done" the GOP because they are mean to Sen. Ted Cruz and not xenophobic enough. They want politicians to adhere to myths and anti-intellectual arguments rather than logic, reason and facts.
Being a "moderate Republican" just means wearing a decent suit, having a "serious" demeanor, and not being too public about the fact that your hobby is biting the heads off of live bats.