Are dogs welcome on nude beaches?
While I don't have experience in it, good judgment would tell me that dogs themselves are reasonably welcome, (on a leash most likely) but their offering piles would be very unwelcome at any populated beach. Although more isolated places would not matter so much, (either piles or leash) So if'n ya don't mind carryin a collection bag and pickin up after them... Same deal for my favorite animal the horse, not allowed on most populated beaches on account of their organic exhaust solids, but the more isolated less peopled beaches are OK.
You may need to check with the local law enforcement authority, however most information regarding whether dogs are permitted on beaches can be found on line. It would be a shame to get to the beach and find "No Dogs Allowed" posted.
I did a search for "are dogs permitted on Apollo beach" with over 3M hits, and found a great web site, bringfido.com, which give you all the information you need.