The planetary society was started by Carl Sagan, funny enough, who according to that site Bill Nye took physics from while in college. The organization seems to be an interest organization more than some official strictly serious business organization dealing with hardcore science. Given Bill Nye spends a good amount of time getting on various media programs and acting as a "Science advocate" regardless of his background, his assignment as a CEO makes sense. Especially since its more of an organizational role as a leader, and not a hard science position. The biggest project of the organization is creating a lightsail spacecraft which, given he is the CEO, he probably wasn't the main contributor. Even so, given his background he would still have the knowledge to help create it from an engineering perspective. It's just a solar sail which you don't need to have a PH.D in astronomy and physics to understand how it works and fully capable of being done by a undergraduate engineer, ignoring actually launching it into space.
Based on that website, even you, if you have an interest in the topic, can join the planetary society.
Memberships
Seems like it is just for adults and kids who have an interest in space exploration and they can join to perhaps contribute or just to learn more about space exploration.