Does my MAAA/FAI membership card entitle me to fly at any MAAA registered club throughout Australia?

No. Every MAAA Club is an autonomous body with their own rules which apply to their operations. Most clubs welcome visitors but it's best to contact the club you plan to attend to check what you need to do to comply with the club requirements. If the club does allow you to fly, your current MAAA/FAI card will confirm that you are automatically covered by the MAAA Insurance policy under its normal conditions when you do.