Mized dancing is not a chumra. Neither is socializing(although I am heistant to say them together, because some uneducated people here will reason that since they consider it so normal to shmooze, they will also think it’s ok to dance or touch them).
This is Modern Orthodoxy’s lack of education at its finest – the difference between MO and everyone else is not the past, but the present.
Being ‘machmir’ means that there is room to be ‘lenient’. There is no compromising on shulchan aruch.
Did you know that according to many rishonim, a man must give up his life rather than socialize with a woman? This seems to be an open gemara about a man who was deathly sick, and the doctors said he would die if he does not socialize with a woman – the chachamim said better he should die. Reb moshe does not understand the gemara to apply to general cases, but only this case – in any case, many rishonim hold that way, and that’s whatthe steipler writes in karyana deigrasa – that might be a ‘chumra’, because it is a machlokes.