The difference is that the information we're talking about here is already completely public information, repackaged in a different format. It would be more like an account that tweets the nearest homeless shelter to you - open information, packaged differently.
Where it might become more problematic would be if the account included inciting language with the information ("here is a homeless shelter, go and mob it"; "Elon's about to land in CDG, who wants to stage a riot"). But I think it's clear that that's not what this account is doing - it's just giving information out that already exists.
And for what it's worth, it's not just Musk who gets this treatment. Most British political events of the last few years have involved journalists excitedly gathering around flightradar24 and watching some poor minister's plane as they make their way back to London to get fired, hand in their resignation, etc. That's essentially the same thing that this Twitter feed is doing (albeit usually more focused on the event rather than 24/7 tracking of one vehicle), but it's not considered a security risk because it honestly isn't. I mean, when the Queen died, Huw Edwards did the same thing for the Princes' plane, and he'll probably win a BAFTA for it...
In all fairness, I have some sympathy towards Musk, as it sounds like he's dealing with the shock of his child being stalked. That's going to evoke a strong emotional reaction, and I can completely understand why he'd want to shut this sort of thing down. But that doesn't make it useful (the information is still public, and anyone motivated enough to track Musk down IRL doesn't need Twitter to find it), nor does it change the hypocrisy of the situation. It seems like he's just lashing out at the wrong person, and making decisions over things that he can control.