As long as you are on public property, you are generally free to protest, providing you do not cause a disturbance or block the right of access of other people.
Handing out food could be problematic, since that may require a health department inspection or city permit. To protect yourself, check with the city, or just don't hand out the food.
You generally have free speech rights per the U.S. and California Constitution, and if this Chick-Fil-A is in a mall, public shopping malls have been seen as an extension of the public square, which expands those rights, even though the property is private.
While you're protesting the company owner's Xtian anti-gay comments, you might also want to protest their trademark bullying. They actually contend that consumers would confuse a kale producer's "Eat More Kale" slogan with their "Eat More Chik'n" slogan.
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