You really should consult an attorney who specializes in non-profits. I know a little about the subject but zero about California law.
Entities like LLCs, S corps, public benefit corps, and C corps exist to shield the owners from the liabilities of the entity. They have nothing to do with tax status. You want to be shielded and also have a liability policy that will defend both the club and any individual members who are sued. When the PI snakes come around, they sue everybody and it is up to you as an individual to fight them off using the shield. That fight costs money, ideally covered by the club insurance.
Nonprofit tax status, probably a 401(c)7 for a flying club, has little to do with whether the club makes any profits or not. Profits are not taxed and may accumulate to an extent; the critical thing is that none of the shareholders can benefit from the activities of the corporation. If you want to see how concerned the IRS is about this, look at all the questions on the IRS Form 990 that attempt to dig out situations where someone is benefiting/aka whether the nontprofit status is fake. guidestar.com is a great place to look at other clubs' 990s. Registration is free and they do not spam you.
Your state may have laws that specifically address flying clubs both for regulating and, again, attempting to root out businesses that are fake flying clubs. Check your statutes.
Sales tax rules apply. For example, everything related to buying and maintaining the airplane(s) may be exempt from tax because the club is considered to be a lessor who is required to charge sales tax on the hourly rentals, dry or wet, again depending on the rules. Dues may also be taxable. Or not. Almost for sure you will have to get a state sales tax permit/registration number.
This all sounds like quite a swamp and it can be if you blunder into the swamp in complete ignorance. But it's like any game; once you know the rules the action is easier to understand.
POA is a great place to gather opinions, some high quality and some not. My favorite internet cartoon:
https://en.wikipedia.org/wiki/On_th...ows_you're_a_dog#/media/File:Internet_dog.jpg Good luck.