They can identify as whatever they want but what they are is neoliberals and neoliberals are conservatives. Meanwhile the people usually referred to as conservatives are radicals. What you might call the actual left are basically the only adults in the room.
So of course neoliberals will say, "Well actually..." because their only real agenda is keeping the actual left down. They honestly don't care nearly as much whether Republicans are in power or not.
The Republicans radicals are less of a threat to neoliberal conservatives because at the end of the day they only make things worse. It's things getting better that would truly threaten neoliberal "left leaning" because then no one would need their conservative failed policies.