Well, for a start, it's a post-scarcity society that has the capacity to produce 7 billion widgets if necessary. So that gets you around a lot of problems.

You'll notice that the crew quarters in the show are decorated in a minimalist style. The only objects people keep are the ones that are important to them. Tools, games, gifts can be conjured as needed and recycled when you're done with them.

Scarce resources do exist, however, especially on a starship: crew quarters are probably not all of the same size, for example. Some people might have to walk a little further to the turbolift (elevator). These sorts of resource allocation problems are likely solved by either a lottery method or based on need. For example, if the Captain gets bigger quarters, it's not because she's the captain, it's because she might need the space to host visiting delegates, etc.

Although I suppose there are still some material inequalities based on rank. For example, ensigns get a single rank pip, while a captain gets four.