It's not only acceptable to keep quiet when your intern is the boss's kid; it's smart, too, lest anything be misinterpreted
Our new intern is the boss's son. Maybe I am paranoid, but I am afraid to speak freely in front of this kid, and so is everyone else in our department. Whenever the intern is around, hardly anyone speaks. It's oppressive. Any suggestions?
That which doesn't kill you will make you stronger, so I hear. Presumably the intern won't be around forever, so grin and bear it as best you can. You are not paranoid, and in the presence of your boss's offspring it is definitely appropriate to keep your counsel. The friendly banter that you and your colleagues might use to let off steam could be interpreted by a young, naive, and loyal-to-his-dad person as negative, or even worse, boss-bashing. So, yes, it's off limits for now.
I am sorry for the young man if he is made uncomfortable by the sudden silence that envelops the room when he enters, but that should be a lesson for him: Never intern for your own dad. That's what uncles and aunts are for.
Keep your chin up, Steve. It won't last forever.