The Turtle eggs are the reason for the rule. Get over yourselves. It's not about being scared, poop or disappearing Dachshunds.
We were staying in Long Key SP this past September, when a lady went out in the water with a Lab two sites over (near the end of the road, with no one on their other side and a vacancy between us). I didn't know there was a rule, 'cause we don't have dogs. Before the dog owner's arrival, a Ranger and I were having a conversation at my site about water conservation and the leaky anti-siphon device on their water supply hose bib. He wasn't overly concerned about the anti-siphon fault, although fresh water in The Keys is semi-precious. I made no comment or even flinched about the new arrivals and their dog, because I was listening to the Ranger talk about his journey from Volunteer to State Worker. I have a slight phobia about un-familiar dogs, due to multiple unfavorable (dog bites hurt and are nasty dirty) encounters in the past that were job related, but I felt no threat and actually thought it was cool to see the interaction and mutual enjoyment between handler and pet. The moment the Ranger turned 'round enough to catch a glimpse of the dog in the water, he excused himself politely, promptly drove his maintenance cart to the offenders' site and informed them of the rules. With little fanfare, the dog was put on a tether attached to their rig and the Ranger went about his duties.
I felt horrible. I wondered if the recent arrivals thought I had ratted-them-out to the Ranger. We have cats. I'm not a dog person, but I understand the bond, attachment, companionship...whatever. I went over to admire the couple's set-up and made mention that I wouldn't rat them out if their dog was loose. The nice lady was cool (also, really good lookin' in her bikini), and shared the info the Ranger orated to explain the No Dog/Beach Rule.
Watch out for Turtles. They may save your life, some day. Turn your camper lights off, too. It confuses the little buggers and makes them head the wrong direction.
Long story short: Perhaps, rules are there for reasons beyond your Ego-centric World. Some people still won't care. Their Momma didn't teach them any manners. If you know someone with baby turtles of their own, help guide them in the right direction by not casting false light.
Don't go to Long Key State Park. It's awesome, and I don't need you suckin' up my reservation dates.
In before the lock.