I think you can mix varieties provided that any fry you produce are kept for your own use. People spend a huge amount of time and effort developing individual strains, and their work can be undone in a single generation.
This goes for Angelfish, discus, goldfish and all livebearers.
I realize mine is probably a minority view, because most fish stores, unless they are really into livebearers, offer all their swords, platies, mollies and guppies in single tanks of assorted fish which virtually guarantees that strains will not remain pure.
Technically, either each strain should be kept separately from each other strain, or each tank should only contain fish of a single gender. And as Gabrielle mentioned, interspecies crosses should be avoided, so platies and swords should not cohabitate, either.