Outdated? So conservatives are only an American phenomenon? Because that’s the only way that conservative = GOP = reactionary. There are conservatives all over the world, and they are explicitly different from reactionaries and usually opposed to them.
That would also mean that the conservatives that exist in America either need a new name or don’t exist. But that’s not the case. They are more or less politically homeles, but many have remained in the GOP because they see it as the lesser evil (for whatever reasons, I’m not here to argue the merit of that belief) or have thrown their lot in with the democrats, but they still exist.