Capitalism is what people do when you leave them alone. You may as well say physics is a religion.
People also steal from and enslave and murder each other when you "leave them alone", in the sense of total unregulated anomie.
To say that people should be "left alone" in that sense is still to take an ethical, moral, or as you've been calling it, ideological stance. To say that nobody should do anything about it; that it is ok, acceptable behavior. Moral nihilism is still a moral position: the position that everything and its negation is OK, that nothing is either forbidden or obligatory.
Now on the other hand, what I think you probably more likely meant to say, is that free markets (which are not identical to capitalism) are what happen when people leave each other alone, in the sense of not stealing from and enslaving and murdering and otherwise violating and exploiting each other. But because people will violate and exploit each other if "left alone" in the earlier sense, i.e. if nobody stops them, then in order to achieve a state where we all leaving each other alone in the later sense, we cannot "leave alone" those who would violate and exploit others.
Freedom requires either everybody to be perfectly well behaved of their own accord (good luck with that), or for there to be enough people actively counteracting the misbehavior of others (but going no further in their actions against those others than to counteract their actions). As Adam Smith put it, a free market is a well-regulated market.
And whether the practices that underlie capitalism (which, again, does not simply mean a free market) count as misbehavior or not, and are in need of counteraction or not, is an ideological position. Should we let people exclude others from the means of production by force, and even help them do so? (i.e. should it be privately owned?). Should we let people demand repayment on borrowed money or goods beyond the return of the money or goods, on threat of force, and even help them do so? (i.e. should contracts of rent and interest be enforceable?) Capitalism answers "yes" to both of those questions; a "no" answer to either would not be capitalism, but could still be a free market.
To lose a free market, you'd have to answer "yes" to "Should we let people demand goods and services from others on threat of force?" It could be argued that allowing that on threats other than force would also lose the freedom of the market. Should we let people demand goods and services from others on threat of the release of private information (e.g. blackmail, I'll tell about your affair unless you pay me off). Should we let people demand goods and services from others on threat of letting them starve or freeze to death because they have no food or shelter? Now it's getting into controversial territory. But no matter what your answer to that question is, you're taking an ideological stance.