So then you get fired, and get another job. Or found a company that ends up dominating the company you got fired from, as the heads of IBM, Apple, and Pixar all did.

American business culture is the same as social culture: association is voluntary, and once either party no longer finds it worthwhile, bye. The flip side of that is that there's relatively little judgment attached to being fired. Future employers may ask a few extra questions to try to determine whether the factors that got you fired from your last job are likely to impact your performance in the next one, but if it really is a matter of cultural mismatch (like a difference in political opinions would be), then you can basically be sure that there is some company out there that doesn't care.