Keep in mind this was a LOOOOONG time ago.
When I pledged it was mandatory to attend the mixer for at least an hour unless you submitted an excuse. Then we were told that nothing that involved alcohol could be made mandatory. With the alcohol free mixers rule now, I would think you COULD make them mandatory, unless it's at a third party event of course. so who knows?
One thing we did say was don't vote yes for the benefit of other sisters - vote based on whether YOU are able/willing to attend. This came about because there were a lot of people thinking "well, I can't go but I don't want to deny everyone else that mix." Mixer time rolled around and only half the sorority was there. IMO it's better to not have the mixer at all than show up half assed. It makes you look really bad in front of the fraternity.
But I can soooooo relate to sisters only wanting to go to mixers with certain groups - we had an older group of sisters that if it wasn't with one of 2 certain groups, they wanted nothing to do with it.