There seem to be a few unaddressed assumptions here. Who is Mars industrializing for? What resources would Mars ever have to justify battling through two gravity wells to acquire?

There's nothing about Mars or early colonies that make inequality any more or less palatable than on Earth. Without severe intervention, inequality would be reinforced by the powerful elites hoping to exploit Mars and Martians.

There's really nothing inherent to democracy that would make a colony more or less successful. In the face of a harsh planet, having an individual leader or at least a small cadre of elites making on the fly decisions might be seen as more welcome in comparison to weeks long deliberations that would come about from direct democracy.