I understand a petition is circulating somewhere online to get Publix

[flvegan]

6. Stop shopping there, if you've not already done so.

Publix isn't going to give any petition the time of day, especially an online one. The only way to send a message is:

Let them know you used to shop there (store, frequency, avg dollars spent);
That as of xx/xx/xx you've stopped, and are now shopping at ______________ because of their policy, and will continue to do so until it changes.

Until they feel it, they'll do nothing. It's the American capitalist way.