Both opinions are so lacking in nuance as to be effectively useless. The rich and their interests are in some contexts the the government, in other contexts they're competing with it.
Look at how Bill Gates relationship with government changes by the year and by the subject for a great example.
The only difference is that the government cant cater totally to Bill Gates, they got a couple thousand other capitalists to take care of in order to keep the country afloat.
The government is the ORGANIZED rich. It's not "everything Bill says goes".
You and me tho, the rest of us millions? We trust strangers that market themselves well, vote and then, just hope they do good by us.
For some rich guys whole point of being rich is to be maximally independent.
Some billionaires are all kinds of weird flavor of Anarcho Capitalist (completely anti government), libertarian (small government), objectivist (suspicious of government and against overbearing regulations and mob control).
Not all, but many.
I think there is an important distinction between independent minded successful people and crapitalists, the ones who collude with the government and enforce their fortunes via regulatory capture.
Not every rich person is obsessed with controlling the world and other people.
Many just want to live their own lives, and want as little as possible interaction with the government.
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.
Look at how Bill Gates relationship with government changes by the year and by the subject for a great example.