A legal opinion is cheaper than you might expect. You might be able to spend between $200-$500 and get a legal opinion from a lawyer. They can tell you, in the context of state and local laws, what exactly the HOA document says about short-term rentals, and where it is silent.
There is another fellow on here that wants to know something about his contract in missouri, but it is a lease so a different situation - but for example in my old neighborhood about 50 people got together for a legal opinion and it paid big - we got about $60K from the negligent devleoper of our subdivision.
Anyway, the other thing to understand is what happens if you do nothing? Does the HOA have the right to impose fines? What fines are specified, if so? Can they file a lien if you do not comply? HOA's vary in their ability to enforce their restrictions, so that is important information to understand too. HOA's also vary in their ability to change their restrictions and bylaws. Consider how much of a process that is for your HOA. For example, if 2/3rds of the residents have to vote to change something, good luck getting 2/3rds of people to do anything in most neighborhoods. If the worst your HOA can do is send angry letters, then maybe that is something you are willing to live with I guess that's what I am saying.
But, finally, just be an active member of your community as a matter of principle. Start going to the HOA meetings. Not to argue about your Airbnb, but just to attend - see what is going on. Participate. If invited, share your opinions in a non-hostile and very logical way.