Home Owner's Associations are just mini-governments. Why is a government consisting of a 4 block home owners association deciding to ban AirBNB okay, but it is not okay for a city government to do this?

More choice within that city for all parties involved. The HOA to decide to allow or not, and those looking for places to live to find ones that match their preference.

I think this is always the main motivation of replacing one-size-fits all government policy with the ability of smaller components governments to decide on their own, for any political issue.

The mini-governments could enact policy that meets the demand of constituent groups within a small corner of the larger entity, vs being forced to follow a "majority" position mandated city-wide that does not match minority preferences.

Most people rent. Airbnb is mostly an externality to landlords, too; as long as the rent is being paid, they can afford to slow-roll complaints about Airbnb tenants.

I understand what you're saying. I'm not understanding who in the current situation has any right to have grievance. In a situation where apartments/homes allow airBnB in their bylaws/HOAs, everyone - the landlords, the neighbors (whether or not they rent) and the short-term renters are all acting in accordance with their legal agreements that they voluntarily agreed to.

In a situation where HOAs/bylaws do not allow renting on airBnb, there already exist proper legal channels for enforcing contracts, and these extra regulations are not needed.

Your comment made it seem like these extra regulations somehow ease these complaints (which you are implying are legitimate). Is my understanding correct?