And you ought to be free to make such decisions for your private associations. You ought not to be free to impose such restrictions on other property owners.
Unless the HOA has the rule at the time every single person in the neighborhood has moved in, then no, it shouldn't be able to make that decision.
HOAs are not democratic governments. They are only allowed to enforce the rules in their charters, and given the power they have, and the ease with which that power ends up being controlled by a tiny group of people, it's absolutely right they're limited in that way.
Bans on AirBNB need to be addressed through the democratic process.