I learned that “capitalism” is an economic system, not a system of government.
Consider for 3 seconds that what you “learned” about the world is a product of the system that produced it
Capitalism is a system of government, and in capitalist countries, they teach their citizens that capitalism is at at odds with the state and not working in conjunction with it
Politics and economics are not independent of each other One explanation
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‘democratic’ is used today a lot of the time to describe neoliberal capitalist governments that are controlled (influenced greatly) by the capitalist class
for example we can look at somewhere like the US and point out how the majority of people in government are all rich capitalists and how through lobbying and campaign ‘donations’ and owning the media the capitalist class controls the government
marxists call this kind of state a dictatorship of the bourgeoisie (capital), as opposed to a dictatorship of the proletariat (workers)
dictatorship here meaning general ‘rule’ not the specific meaning that the word has taken on more recently
so ‘democratic’ capitalist countries that exist today are under the “rule of the capitalist class” or “dictatorship of capital”
so if you wanted an actual democratic (in the real sense of the word) government, you’d need a government which is controlled by the majority of people, that is, the workers, a dictatorship of the proletariat
under such a system capitalists cannot be allowed to have influence on the government, which is something that is not really possible unless you implement tight capital controls like they do in China
the reason being that capital flight is a very real threat to a capitalist economy, and having that power over a government lets the capitalist class dictate terms and change laws to be favorable to them despite what the majority of people might want.
so to answer your question, the only way to have a government with a capitalist system not be controlled by capitalists is through suppression of the capitalist class, if they are allowed to have influence then you no longer have actual democracy.