Are you not aware of FedGov statutes that regulate FedGov employees from engaging in partisan political activity ?
You are referring to the Hatch act, an act you apparently don't understand that well.
The only real restriction the Hatch act places on federal employees actions is that they can not host a political fundraiser for a candidate for a partisan office. It also restricts you from using government resources (computers, office equipment, time, etc) for partisan electoral purposes.
Finally, and the only thing that could be remotely relevant here is it restricts employees from using their government position for partisan purposes. IE he couldn't say I am a DOJ lawyer and you should vote for candidate X.
In this cases none of it applies. My understanding, not a lawyer, the hatch act deals with electoral activities. Booing someone you don't like is not an electoral activity. Federal employees also don't lose their free speech rights as long as they aren't explicitly identifying themselves as a government employee, which from the account provided he is not in the facebook post describing his booing.
Now was what he did smart, no. Should he have publicized, even on facebook, what he did, no. Should he be punished for it, no.