They aren't random, they are DOGE employees. And at the moment, we don't even know what the role of DOGE is in the US government. Is Elon Musk a cabinet member, despite not being confirmed by the Senate? If DOGE exists solely as an advisory body, then why do they have the power to fire employees of other agencies (which have been ratified by Congress)?

So rather than being upset about posting public email addresses of public employees, I would say the disservice to taxpayers is allowing an unelected agency to make decisions about other agencies with no Congressional oversight.

As for "is there a law" I think this is implicit in the nature of representation. If you vote for someone to represent you, and after they are elected you have no way to contact them, how do they actually represent you? I'm not suggesting people should harass DOGE employees or say bad things to them, just that we need more transparency in general.