I just responded to a similar question that appeared to involve an HOA, but your question at a condominium raises some additional issues.

One, a condo association cannot use its rules and enforcement powers to restrict your access to the condominium unit. That prohibition is expressly written into the Georgia Condominium Act. While association can use rules and restrictions to push compliance with rules, condominiums are limited on depriving an occupant of access.

Two, the current health crisis should make associations rethink how they are dealing with access to units. A rethinking of normal rules is certainly justified for the health of all the owners in the community. Under the circumstances, a call to the county health department might get you some results, or maybe a call to the condo association's legal counsel would be needed or helpful.

Three, from a more legal perspective, there are many associations that don't follow their own rules in imposing sanctions (such as cutting gate access), and there can be remedies along those lines. At the moment, however, a more practical and quicker option is probably better. If the association is unresponsive, and if they won't back down by just giving them another copy of the piece of paper they are asking for, start with a call to the health department. If that doesn't work, talk to an attorney who can contact the Association's legal counsel by phone. The last alternative would be going to court, and that is both expensive and not very practical with the courts basically shut down due to the health crisis.