The information is available on the website of the airlines. In any case, the person at check-in told you his airlines's policy.
American Airlines say:
For example, if you are taking golf clubs with you, you will be charged the same fee as the 1st or 2nd baggage fee of your destination. You can travel with 1 golf bag with up to 14 golf clubs, 12 golf balls and 1 pair of golf shoes. If the golf bag contains anything other than the approved items, additional oversize and overweight charges will apply.
Presumably, these are the same "Boy Scouts" who try to protect you from terrorism.
Members should take preference above guests at all times.
You should have advised them that you were playing thru at the 9th tee. If they complained about it to the pro, he should have advised them they are welcome to not come back.
I wouldn't pay membership dues to a place that doesn't put members first.