I think one of the earlier posts had it - for situations where the membership needed to vote on executive, policy, or other aspects - people coming in the hall had to show a membership card to prove they were eligible to participate in a debate and vote. Presumably for privacy (in those days, for some reason, leftist groups could be paranoid about police spies) in some cases the general public was not allowed in to observe. proceedings. I assume membership cards in many organizations required paying dues, and the expression “card-carrying” implied the person was more than an occasional sympathizer, they actually put their money where their mouth was and were fully committed to the aims of the organization.