There are no requirements at any local league that I know of which say "you must be a club member to play". That wouldn't be very nice at all in my opinion. The Doubles League at Schroeder Park is open to anyone who shows up with a little money for the night.
That said, it's the hope of the St. Louis Disc Golf Club, and other area clubs, that you do eventually choose to become a club member. We're not like a traditional "club", where there is some pre-qualification that a person must meet before joining, we're more of a volunteer organization who's purpose is to support and grow the sport of disc golf in the St. Louis region. Our membership fee of $20 is actually more like a fund-raiser, because all of our membership dollars go directly back into building new disc golf courses and maintaining the existing courses. Heck, this is going to be a really important year for our membership, we're paying for and installing 2 (maybe 3) new 18 hole courses all on our own - and it's really expensive.
So, sorry for the longer than expected answer, but we're glad to be here for you and hope to call you a member whenever you're ready. I'm open to come out and meet you anywhere you like if you're interested in joining, I have member tags and discs at all times.