I think there's a case to be made for not letting people near a karaoke machine when they're raging drunk... once you've seen the chorus of "I Will Always Love You" accompanied by a sparkling, lime-green fountain of projectile vomit and a loud thudd as the 'singer' falls of the stage in a wildly flailing, uncoordinated spasm of inebriation... not pretty.
If you can sing the words, and keep the contents of your stomach where it belongs (not all over the unfortunate onlookers), it shouldn't matter about gender, age, sexual preference or anything.
I hope the complaint is upheld. That was totally out of line.