I don't think you have any sort of expectation of privacy when you go to a public location like a restaurant or a store, and I don't think the ruling in Dobbs, however it turned out, would have changed that.
That said, Kavanaugh's issue in the restaurant can be handled in other ways. First, the restaurant owner can simply ask the protesters to leave, when they don't, call the police and have them trespassed. That was probably the correct way to handle it. If they don't do that, then if I'm Kavanaugh, I simply find someplace else to eat where the proprietor has more control over his facility.
There is also probably some sort of harassment/restraining order process in Maryland that Kavanaugh can use to prevent individuals from harassing him under some threat of jail, but I don't see a SCOTUS justice doing that.
I agree with slapshot that I am generally opposed to the public harassment of people, any person. If I saw someone in a restaurant with whom I strongly disagreed politically, it would never dawn on me to go up to them and berate them publicly, but that's just how I was raised. I have a sneaky suspicion that most of the people on this board would be the same way, probably because that's the way they were raised too.