Not tied to a specific political system. IOW both democracy and communism can have an economic system base on capitalism.
It seems to me that the key component of capitalism involves a government guaranteeing property rights, to some degree or another. Property rights relate to a philosophical position, which would make it political, in my opinion.
Under such a system, a government need not guarantee any other rights, such as freedom of speech, freedom of religion, the right to vote, the right to keep and bear arms, the right to be free of search and seizure, etc. All of those can go away under a capitalist system, as long as private property rights remain. The government's main essential role then becomes protection, whether it's national defense or domestic law enforcement. That, and mediating contract disputes.
It doesn't even have to apply to everyone, nor does it need to guarantee fairness or equality. That's how countries like the U.S. could still have slavery and be considered capitalist, since white male property rights were still guaranteed.
After all, if capitalists are going to invest anything at all, they'll want some reasonable assurance that the government isn't going to seize their property and take all their money. Capitalists don't seem to like things like that, however amoral they might be. Above all else, a capitalist system relies upon that promise from government (or whatever political authority happens to be in place). Without that, capitalism isn't possible. Of course, there are societies which may exist underground, outside the law or outside the realm of any established, recognized government. But even they might subscribe to some alternate form of social contract, depending on the society and their set of values.
It can be said that politics is as essential to human interactions and transactions as much as language is essential.