Barbecue Grills on STT Beaches

Can one take their own portable BBQ grills (charcoal/propane) to beaches on STT? For example, Magens Bay, Smith Bay Park, Brewers Bay.

I have seen people bring their own BBQ grills (tabletop/stand-up) to Lindbergh Bay.

I would like to know if you can bring your own grill to pretty much any beach one can visit. Or are you restricted or need some kind permit you have to pay for or not pay for.

I'm not referring to gas grills that are mosty used at home on your deck/property.

Thanks in advance!