If so, these Christians should sue the Villages for "religious discrimination."
HOAs can impose all manner of restrictions, but they must be enforced equally, without discrimination against any race, religion, gender, etc.
My HOA will let you put stuff on your balcony, but nothing can be permanently attached. So you can put up some plants to block people from seeing you while you're on your patio, but you can't put up fencing attached to the railing even though the result is similar.
The devil is in the details.
Fortunately all of the units in my HOA have stairs so there are very few retirees here. So the rules are far less onerous on us than the Prisoners at The Villages.
Sumter County, where The Villages is located, is strongly Republican, being carried by Trump by a more than 2:1 margin in both 2016 and 2020. The big margin is attributed to the retirees in The Villages. The problem is likely the HOA authoritarians.