The question stll stands unanswered.
I believe it will remain so until we can see the HOA constitution and the lease agreement.
I believe this falls completely under contract law. What does the contract say? I believe that while a "no guns allowed" clause may carry no legal weight a property owner may ask an occupant to leave. Failure to leave when asked is trespassing. Someone might feel that being asked to show their permit to carry weapons to stay on the property to be unnecessary but if those are the conditions then comply or leave. Much like places that have a dress code to enter, or be of a certain age, or any of a number of conditions to enter, it's private property and people may be asked to leave for any reason.
If redsox wants to take this to court and get legal precedent in Iowa that people that rent or lease property can be armed on that property, without having to show a permit, then I welcome it. Just be sure to get some smart lawyers so that this case doesn't screw it up for the rest of us.