The democrats are also a right-wing party, just less so than the republicans

This, 100%.

There's a false narrative that everything and everyone is either left or right, liberal or conservative, blue or red. But it's simply not the case.

There are a handful of leftists in the Democrat party, but the vast majority are right wing conservatives. The Overton window has shifted hard to the right and most of the Democrats shifted along with it.

A Democrat politician today would have been considered a right wing republican extremist 40 years ago.