MUD is a very rigid system, which basically allows for D&D style games, and little else. In MUSH, MUX, MOO, and other similar setups, the actual codebase is lighter, which allows you to do more actual coding. In practice, this means that it is easier to simply go to the master 'room', and code in the commands and mechanics for Shadowrun, and then it would filter out to the rest of the rooms. There are also widgets you can make that will allow you to do customized charsheets, and the like.
Just because MUSHes are typically done for freeform or semi-freeform games doesn't mean they can't be used for things like Shadowrun or D&D. It would be significantly more difficult to code a MUD to fall in with SR3, much less SR4.