Yes, the Y may refuse to process your application or accept you as a member unless you sign the waiver. The Y is a private (i.e. nongovernmental) entity, and there is no inherent right to be join it; the Y accordingly has a right to put reasonable terms and conditions on membership, so long as it does not disriminate against certainly classes of people (for example, no racial discrimination in who may become a member). Those terms and conditions could include requring a waiver to be considered for or become a member.