Why does it not feel like right wingers are in charge of the country?
Because we are not. George Soros donated $32B to fund his Open Society Foundation of which he is the Chairman; it's his, but he gets tax advantages and uses the proceeds to push his socialist/collectivist policies through the media and the education system. He also benefits by betting against the currencies of the countries he destroys (e.g., England, Indonesia) In my estimation this is the worst player, but he is not alone.
I don't know of any similar effort on the part of people with individualist/ capitalist principles. Koch family is an example of the fake right using their money simply to benefit themselves through the oil industry without regard to the damage they do to the rest of the world.