What is politics? People spend have their waking hours in a strict top down system, instead of a democratically organized economy. Tbf that’s not only true for Capitalism but also for Soviet style socialism.
For example, the market may “decide” that asbestos is the best insulation, however, the market does not set political policy about insulation.
The market is not the only aspect of capitalism. Plutocracy is another strong one. Being rich makes you influential in capitalism in contrast to systems where your ancestry is important or systems that try to get rid of power altogether respectively try to distribute it as evenly as possible. So while I said it’s compatible with monarchy and democracy, this is true on a scale. If the monarch is listening to rich people instead of their kind, it’s less monarchical and parliamentary democracies are more prone to capitalism than more direct forms of democracy.
To put it differently: it’s not only about who makes the decision according to the constitution, it’s also about how this decision comes about. Besides: the institution at least makes capitalism possible, if not enforces it in one way or another. The existence of a state alone is something capitalism needs, a punitive justice system that enforces property rights, which often also are constitutional themselves, …