Are Dogs Allowed at Farmer's Markets in MA?

Seriously - can someone help me figure out the actual law here?

This past weekend, I went to a farmer's market in Westport that was held in a parking lot. I was with my mom and fur-kid, who was leashed and walking by my side. Shortly after we walked in, a man came out from one of the tents and told me dogs weren't allowed at farmer's markets "per Massachusetts' state law because there is food out."

I didn't think too much of it and left, taking doggo with me. When I mentioned it to some people later in the week, no one could believe that dogs "aren't allowed" or had ever heard such a thing. I can totally understand asking someone to leave if their dog was knocking over tables and eating all the vegetables. Or if it were indoors. If the argument is fear of an animal contamination, I am confident most farms where the produce came from in the first place are home to a dog or two. And if I'm buying produce from a market, much like a regular store, I'm washing it at home before I eat it.

To me, a farmer's market in a public, outdoor space is essentially like a park or street, and is A-okay for dogs. But I'm no expert on MA state law. Can someone clarify or confirm?