It wouldn't be stalking, but widely disseminating even public records could easily be construed as doxxing, which is not accepted on most public, reputable forums.
The myriad of flight tracking websites are not in violation of any doxxing rules whatsoever. There is no dissemination of public records other than replaying info as-is.
The existence of these automated tracking accounts have no effect on Elon's personal safety because any hypothetical bad actor would not need to depend on this singular account on a singular platform to obtain such information.
Public records are public records, doubly so if they concern billionaires. Musk has been begging to be a public person for decades now, he does not get to decide the framing
You drive your car around in public with identifying information on it, anyone can derive a record of its public movements if they were inclined. For example by just following you around on public roads and streaming it, like how paparazzi operate legally.
You have to transmit your license plate information visually as you drive, so I don't really see the difference. The fact that some data is public doesn't mean shining a spotlight on specific elements easily is an appropriate thing to do.