But there is an element of faith in the market. If the capitalist read the Wealth of Nations or not, s/he believes in the invisible hand and that free markets are the right way to manage our lives. It is the ideological package that guides people who embrace capitalism as their way of life.
A capitalist has no need of believing capitalism is a good way to manage "our lives". The capitalist simply acts in their own self-interest. I think Karl Marx and Ludwig Von Mises would agree on this. Marx would consider the system evil, Mises would consider it good. But neither would consider it "faith based".
The piece you’re missing here is that the capitalist theory is that things will work out well on a macro level when everyone is acting in self-interest that is the key to capitalism as an economics (more specifically as an acceptable mode of the economic term in “political economy”) and it is the only reason it is seen as acceptable. The whole reason capitalism is seen as “rational” is because of this argument, if the only thing that were claimed is that “everyone should act in self interest and who knows what will happen” no one would accept it as a reasonable economic system. Capitalism took root because of this notion that rational agents acting for themselves would necessarily (with no evidence to back it) lead to the best scenario (the idea of the market dictating whats best for mankind through what it desires, supply and demand). It is also its article of faith, which mounting evidence (see climate crisis) argues against.
Marx’s whole point was to argue why this proposition was false (why “everyone acting according to self interest” actually led, in spite of the good it produced in the short term, to longer term evils, like proletariatization, exploitation of workers, concentration of wealth, etc. though Marx did not forsee (and couldn’t of course) the catastrophic effects self interest would have on the climate)). The whole point is that the progression of capitalism up to this point has proven we need more than just “self regulating markets or self interested “rational” agents” since we’ve come to see the absence of other shared values leads to species level existential threats (again, climate).