I'm part of a nation wide historical group that is a filed 501c3 based out of California. Recently the topic of accommodations for disabilities has come up and while our by laws state we will follow the ADA the belief that it is classified as a private club comes up again and again. Anyone can buy a membership online and those not holding a membership can still attend by paying a five dollar surcharge. So are they classed as a private club?
See excellent article (starting p. 10) which will give you additional assistance in determining if your club meets the requirements for exemption.
http://www.cmaa.org/uploadedFiles/Member/Legislative/ADA.pdf
You don't provide enough facts to say if this is a bona fide private club or not. It is more than merely membership. Generally, anly bona fide private clubs that are open to only members and their guests, do not regularly hold public events and are tax-exempt under the Internal Revenue Service’s 501(c)(7) or (3) may be exempt from ADA regulations. To know for sure requires legal review.