Does the behavior during this office pet controversy rise to the level of bullying?

Q: Our company president allowed two people in the office to bring their rescued dogs to work until an incident caused us to disallow animals of any sort on the premises unless they were service animals. Within minutes of announcing this new policy via email, an affected employee came to my office and gave me a "piece of her mind,” standing very close to the door as if to block it, breathing very heavily and waving her arms around, and saying that she was not leaving. Afterward, I thought all was quietly settled until one of the employees posted a store-bought sign in front of her cubicle reading "Beware of Dog.” I'm feeling very uncomfortable and expecting retaliation. I believe that what the employees have done falls under the description of workplace bullying or harassment. What do you recommend? – Anonymous, California