Well, it matters a whole lot once you choose to bring up "One share, one vote" in response to "One person, one vote", since it shows that it's either wrong or shows a gross misunderstanding of democracy.
A hypothetical country with multiple classes of citizens that had different rights and voting powers would not inherently be undemocratic. It's not something I'm in favor of but equality != democracy.
IMO it matters roughly as much as it's common. Do you know any country where, say, 10% of public companies have non-voting stock your can buy and voting stock your cannot easily buy? 20%? 50%?