I would do everything and use every resource I have to try and make happen a society with classes abolished. Maybe start by forcing no private property over production means using the Securitron army, so work exploitation is no longer a thing.
There would be no central government, only one major rule enforced by securitron army: no work exploitation, no profit allowed. This way, everyone would have access to everything that is produced, and what would guide the production would be the idea of common good. What religion was to the Middle Ages, common good would be to New Vegas. So, it would make no sense in Mojave people stealing from each other, as everything already belongs to everyone, just go there and take what you need, contribute how you can to make everyone life better.
Money would be completely abolished. You just take what you want, as long as it doesn't fuck with the society or affect the common good.
The securitron army could also be useful to enforce local village laws, for example, Goodsprings people made a bunch of rules and laws on their settlement, the police force that would help enforce said laws could be securitrons. Point being, everyone has access to the best technology that New Vegas and Big Mountain has to offer.
I believe that education would play a major role in this Mojave, so groups like Followers of the Apocalypse would play a major role. In my free New Vegas, everyone is equal, humans, ghouls and Super Mutants. I believe that we all have a lot to learn from Super Mutants and Ghouls, they have seen some serious shit in their lifetime, and the Master is a great experience that the whole Wasteland can learn a lot from.
From there, the idea would be expansion of this idea to the whole USA. New Vegas would embrace those who need a place to live and work, and obviously help other places get rid of work exploitation as well by encouraging revolutions, or maybe if necessary, waging war against class divided societies that might get into our way. I mean, New Vegas would be a fucking powerhouse, its a big BIG chance to apply a class abolished society and not failing, it has firepower and manpower, big factories, great research institutes, amazing medical facilities etc.