On one hand, I agree with you. I've personally seen low level people at a large corporation believe they were unequivocally in the right, and tried to use the weight of their moral conviction to impose their view of things onto everyone else. It's not your job to do this, and it's not my job to care.
On the other hand, there has to be some capacity for this type of discussion to occur. Musk owns less than 50% of SpaceX, and I generally think employees should have some manner of input into the operations of the company they work for. History is full of cases where the justified party tried to convey their problems politely, were ignored or quietly silenced, and had to raise the problem loudly to get any traction. I think it's a reasonable desire to want to work for SpaceX, but not want someone's first reaction to hearing that you work at SpaceX to be bringing up whatever stupid thing Elon has done this week.
If someone has the answer on how to find this balance, please popularize it. In the meantime, I've left the large corp I was at and joined a small company with 7 others where I don't have to deal with such problems or such activists.