I would think Trump could also issue an EO to exclude companies from government contracts that engage in political discrimination. The EO should deal with discrimination and not just single out specific companies.
This problem is likely not limited to tires or Goodyear.
It isn't just political discrimination. It is flat out racial discrimination which is already illegal. How is it possible that banning statements on racial equity, their allowed topic, that relate to races other than "Black" does not create a hostile work environment. Just imagine if some company said you can wear a shirt that says "All Lives Matter" but you can't wear a shirt that says "Black Lives Matter".
Nobody would think that was acceptable and the DOL and DOJ would be filing lawsuits the next day.