Based on a web search, I think this is the law referenced on the LAFB sign:
Also, the show part of Ellington Field is not a "secure area". A secure area is only part of a commercial passenger airline terminal where you have to pass through a TSA screening to enter. Ellington does not have a passenger terminal any more.Title 18, United States Code, Section 930
WEAPONS PROHIBITED
Federal law prohibits the knowing possession or the causing to be present of firearms or other dangerous weapons in Federal facilities and Federal court facilities by all persons not specifically authorized by Title 18 United States Code, Section 930(c) Violators shall be subject to fine and/or imprisonment for periods up to five (5) years
(1) The term “Federal facility” means a building or part thereof owned or leased by the Federal Government, where Federal employees are regularly present for the purpose of performing their official duties.
Therefore, in my (non-lawyer) opinion, you should be able to legally carry at the airshow, as along as you stay out of the federal buildings.
Therefore, in my (non-lawyer) opinion, you should be able to legally carry at the airshow as long as you stay out of the NASA or military buildings.
Keith