Anybody can take photos or videos in public area, so does the government. If you are so paranoid about your privacy, stay at home, order online, simple as that.
1) The government can track me everywhere with cameras anywhere they want in public; companies would be mostly restricted to when I walk past their franchises in most cases (drones could be an issue, but cross that bridge when we get to it)
2) The government agencies have motivation and a history of suppressing new or bothersome political parties which challenge their budgets. Ether by spreading dirt gathered via other activities or jailing activists such things are at least substantially harder for a company to accomplish.
If you are paranoid and not a good make-up artist, you may have to settle for glasses and clothing with integrated LEDs designed to confuse known recognition algorithms. Or maybe just start wearing masks and veils in public.
They might be able to track John/Jane Doe #1 across a plaza, and maybe match that up across multiple cameras, but without a reference database connecting gaits to public identities, there is a possibility that without reasonable suspicion, the data for John/Jane Doe #1 would have to be purged before it could be linked to you.
Of course, a state-level actor that chooses not to obey the law could retain those data indefinitely, and eventually identify you via statistical analyses. If you don't want that to happen, you will need to get politically active and make public oversight of agencies that perform surveillance of the public an issue.
Otherwise, you might have to wear specialized clothing and shoes that change heel height and sole shape as you walk.