From my point...if the beach says no dogs...than there should be no dogs! end of story.
There is not one rule for one and no rules for the rest of the state.

From my maternal point...your littlies, only have one face.
Dogs can carry scares well and often are commended for
their battle wounds by their brilliant owners.
It only takes a second for them to maul and rip at a face. (which is at their level)
And then there's the mental scaring!
Just ask an adult that does not like dogs..
it will usually stem from a inconsiderate owner
that had their dog at the beach when they were young.
It only takes one growl or bite to scare a littlies for life.
Dogs have their place (I love dogs) but not on a beach that says NO ANIMALS!