The GOPe has shown itself to be liberal. I don’t think they have gone all the way to ‘progressive’ yet, because I see ‘progressivism’ to be a direct heir of Stalinism. Liberalism, though, is also a terrible disease, and I wouldn’t ever trust a liberal with my government.
One tactic the elite use to maintain control over populations is to have "the vote" and to give people superficially different choices. The elites who pull the levers of power and information will see to it that there is enough difference between the choices, so as to entertain the people, and to lull the people into a sense that their vote makes a difference.