I'm not talking about a small capitalist with a nice house and a nice car.
I'm talking about the super rich.
Thr super rich have to be the government to be super rich and the little capitalists just ride the wakes made by the big guys.
These ideologies you mention are just political stances made by the rich in order to promote their measures amongst the poor.
Objectivism was made by Ayn Rand and it was promoted so much because it defended capitalism. They disseminate these ideas in order to promote their stances.
Libertarianism and ancapism are inconsistent because it pretends that large capitalists wouldnt immediately organize themselves into another large state power. A state is necessary to not have all out war between the powerful.
Ask any political science major and they dont take these ideas at face value because these ideologies cant exist as such.
They are more like life style politics than real political frameworks.
I suspect the reason they are even espoused is because they represent an immediate weakening of government regulation that can increase profits. The capitalists want people to think it can exist so they can have more power.
But a true libertarian or ancap reality is a pipe dream. Its true purpose is to create less oversight and thus more profits. Your average Joe, like you or me, has about 0 benefit from this.