Dreams about being naked in public often symbolize feelings of vulnerability or a fear of exposure. In your dream, running towards the beach naked suggests a desire for freedom and a willingness to embrace your true self or desires. The beach can represent a place of relaxation and escape, while the act of skinny dipping indicates a longing for a deeper connection with yourself or a desire to break free from societal norms.

The presence of the family and their dog may reflect your concerns about how others perceive you. Their reaction—seeing you but choosing to ignore you—could indicate a fear of judgment or embarrassment in your waking life. It might suggest that you are worried about being exposed in some way, whether it's related to your personal life, your emotions, or a situation you're currently facing.

Running back for your clothes signifies a retreat to safety and comfort. This part of the dream could point to your need to protect yourself or to hide aspects of your identity or feelings that you may not be ready to share with others.

Overall, this dream might be encouraging you to explore your feelings of vulnerability and the balance between being open and protecting your personal space. It may be beneficial to reflect on any areas of your life where you feel exposed or judged, and consider how you can embrace your authentic self while navigating those feelings.