In what way is the Republican party progressive? They're so categorically anti-progressive, they use the term as a pejorative.

The Republican party has yielded on basically every issue in living memory. They're the Democratic party with a built-in time delay. They only exist to bring up the rear of what is acceptable in the Overton window, not promote any policy of their own.

If you want examples The Republicans fought the New Deal hard and then dropped it. The Republicans fought the Great Society and then dropped it. The Republicans fought gay marriage every step of the way and now recently have members voting for the Respect for Marriage Act.

They don't present policy, they just fight progress de jour until it is time to move to the next thing that needs opposition.

They bow to popular opinion. They use wedge issues to maintain power and control which is what it is about. That and grifting.