In general, capitalism can coexist with democracy, but there is definitely a tendency for unchecked capitalism to challenge democratic ideals.
Capitalism can coexist with democracy because both are very much concerned with preserving freedoms. Capitalism is all about people doing whatever they want with their property. Democracy is about people having political and personal rights. Even though property rights are not necessarily the same thing as political and personal rights, both capitalism and democracy center on preserving people’s rights and limiting what governments can do.
However, unchecked capitalism can definitely challenge democratic ideals. One democratic ideal is that all people have to be equal in the eyes of the law and equal in their ability to have political influence. Capitalism tends very much to tear down equality. Some people get rich and become powerful and influential. Others are less wealthy and therefore less influential. This challenges a major tenet of democracy.
Thus, capitalism and democracy are not completely incompatible, but they are at times in tension with one another.