I came up in Sindome during a time when the playerbase was less than 1/4 the size of today's, and, the "segregation" was much, much more rigid.
The playerbase is large enough. If people are avoiding roleplaying the theme, "not finding enough players in my sector" is not the reason.
There is a certain theme to the game. You know it before you create an account and roll a character. The theme is:
Up topside, Corpies are disgusted by, and fearful of, Mixers. Even more than they fear Mixers themselves, they fear losing what they have and becoming one themselves.
Down in the Mix, Mixers are resentful and fearful of Corpies in general and Corporations even more in particular. Even more than they pity Corpies individually, they fear the Power and resent the oppression.
Now. I completely understand some players' desire to RP with characters from the other side of the maglev tracks. But if you're a Corpie, then, having a group of Mixers to visit, or, worse, crash at, your Central Green-sector condo isn't themely. What's themely is meeting them clandestinely, far away from your regular haunts because business like this should be kept out of sight of your neighbors and co-workers. Maybe everybody has a favorite courier, ponyboy or pusher, but they don't treat them like they aren't scandalous at best and dangerous at worst. The fact that you, as a player, trust the other player not to have their character rob yours when they get together for ice cream, poetry or blow jobs doesn't mean your character shouldn't think their character won't.
If you're a Mixer, then, having your Bitch'n Chik'n-eating, dogmeat-selling street-urchin character cozy up to your nice friends at Grunen's isn't themely either, unless you're working on a swindle. After all, that's what Corpies think you're all up to anyway. If that Corpie is really your friend, would you embarrass them by allowing them to be seen with you by their neighbors and co-workers? It'd probably blow your cover - you're more likely to get away with taking advantage of them if you keep the association quiet till you get what you need from them.
Fine, fine, everyone can point to Romeo and Juliet as a case study in crossing boundaries because humanity can transcend them. But Corpies and Mixers aren't "roses by another name", and Sindome isn't a love story whose moral is about overcoming prejudicial obstacles.
There are reasons within the theme for Corpies to associate with Mixers, but carefully and discreetly. There are reasons for Mixers to associate with Corpies, but primarily those reasons should be for profit or advantage.
Subverting the theme is one part of my argument about why ignoring the class divide is poor gameplay. The rest of it is about stuff I'll lump under a label of "agendas" - which is to say, fluff, plot, roles and goals.
Theme-wise: Unless your characters are using this class-mixing to drive agendas, then you're literally ignoring the Lore, the theme, the in-character history, and the very nature of cyberpunk just so that you can play besties with everyone and avoid roleplaying behaviors which you might be uncomfortable with as a real-life person in the real-life world. It's a game - playing the game as presented is gutsy and sporting.
Agenda-wise: Cooperative competition is about cooperation AND about competition. Mixers who aren't using Corpies and Corpies who aren't using Mixers are all cooperation and no competition. You aren't helping each other get anywhere, you aren't giving each other challenges. Now: I understand that not everyone here plays to "win", or even to get their characters ahead. That is completely fine. There are many different things which different people might or might not regard as "winning" or as "progress" and there are a variety of different kinds of people who play the game. People can have different kinds of OOC goals about what they want from the game, and different IC goals about what they want their characters to achieve. But the game structure is something to take advantage of, not something to ignore. Ignoring it will undermine what you can achieve with your character.
Fluff, plot, roles and goals. You can pursue fluff. People do it all the time. The ones who do that the most tend to be the least involved in plots - player-driven or GM-driven ones. When your role is poorly defined, it's hard to engage others in the kind of play which drives cyberpunk stories. The strongest progress toward in-character goals tends to be made by players who are very clear about, and committed to, their character's nature, niche and values.
For most of us, the top "agenda" is just "good RP", right?
But to me, "good RP" is honoring the parameters we're given and playing the role we choose to play within those parameters.
Here's a radical thought:
If you have characters who are so committed to mixing company and crossing the class barriers, why not have them drive exciting, dangerous, compelling stories about doing so? Make them dissidents, activists, or martyrs. Does your Corpie really love some Mixer that much? Be willing to see her lose her job over it. Does your Mixer even really like Corpie company at all? Then have her climb out of the Mix, because a real Mixer breaks out in hives if forced to endure an environment like Grunen's Tavern. And maybe both of them should be aiding, funding, or joining the insurgents and provocateurs who have the brass and the integrity to take direct action against the oppressors, if they feel so strongly that Mixers deserve respect and rank-and-file Corpie drones are just victims of the same power structures.
(Note: Where I use the word "you" above, it's the impersonal "you". I don't know Barrien's character and am not speaking about any other specific player or their character either. None of you are one-dimensional, even if this question and my answer might be.)