The humor in these skits is based on the fact that gender identity is so important to our social selves that we can barely interact with anyone without first determining that person’s gender.
Given that people didn't know whether Pat was female or male, they could laugh at all the things he or she didn't because it confused them as to what his or her gender really was. This is because the first thing we notice about people is whether they are male or female, and we are confused if it is someone 'in-between.'