Well, book burning is kinda dumb because most of them, if not all, are already digitized. It's a statement at this point in time. While really stupid and backwards, expression is still a right and freedom that Americans enjoy.
This is unlike other countries where you can be thrown in jail for something even lesser and never have a recourse or trial.
Of course they can. They might get in trouble or even fired. But they can still say whatever they want. They are also protesting on both sides of it, too, as is the right. The great American discourse.