I see a distinction btwn (A) a shift in public rhetoric, ie the Ratchet Effect on the Overton Window, & (B) the ideological consistency of federal policymaking of the Duopoly.
The latter is identifiable by aggressive expansion, corporatism,& anti-democratic practice here & abroad
Some of them were actual Republicans at the time. Then Chuck Schumer, Nancy Pelosi, and Steve Israel recruit them to run in Democratic primaries against actual Democrats.
When I was growing up, they were called "conservatives" or "right-wingers", because that's what they are. There used to be liberal Republicans and conservative Democrats and no one pretended otherwise. Then they invented the terms "moderate" and "Centrist" to hide it.