First of all, California isn't just any state, it's the largest one. It even has stricter auto emissions standards pushing forwards the rest of the country -- so this isn't so much a dangerous precedent, as a "special California thing" which is historically more protective of the consumer than the federal government. (I personally see this as a positive thing.)
And as long as state laws are limiting abusive behaviors, I don't see what the problem is -- then we all follow the new "floor" and the whole country benefits. A small start-up can not choose not to lie about a bot being a person just as easily as a tech giant can.
The problem is if local laws conflict with each other or impose a significant burden. But then the federal government generally steps in quickly and shuts things down thanks to the interstate commerce clause.
So I don't think there's anything to worry about here.