Hmmm, its tough to come up with rules that make sense in the context of communism yet fit within the game mechanics while adding challenge.
Here are a couple that might make things tougher and ape communist ideals. The whole equality between all classes idea can be taken to serious extremes and should make for some FUN! scenarios.
Set the rule so that all dwarves receive the same exact material possessions making only mandatory job related changes to this standard issue dwarf gear ration. For instance, you want to give your legendary axe dwarf full masterwork steel armor then you must have masterwork steal armor made for and equipped by every single dwarf in your fortress from the lowest peasant to your greatest warrior. If you want to give him a masterwork steel axe then you must have masterwork steel weapons for every single dwarf in the fortress that can weld one or at least weapons of comparable quality and value such as a masterwork silver hammers for hammer dwarfs.
Also everyone is in the military. EVERYONE. It would be unconscionable not to divide up the burden of fortress security equally between all dwarves, able bodied or not. There must be no preferential treatment when assigning dwarves to squads. Your elite fighters, incompetent farmers, mayor, bookeeper, legendary armor etc. get randomly assigned together in mix matched groups of all social standings. There is no putting all your more important dwarves into separate units that get to hang back and play it safe in a siege. Everyone is equal. Legendary Armorer and useless peasant will fight and die side by side.
Treat the capitalist scum you encounter in the only way fit for such barbarians. Kill them all, every last money grubbing merchant that shows up must be executed and the spoils equally divided between everyone in the fort.
Healthcare for everyone. This means staffing an absolutely huge hospital. No injured dwarf should ever go without a hospital bed, crutch etc.
You must never show favoritism towards any dwarf for any reason. There will be no sacrificing lesser dwarves to save more valuable ones. Each dwarven life is worth exactly the same. Even children.
Although these rules are few in number and quite simple it should actually make things a lot harder while sticking to the theme pretty nicely.