You're correct, being the CEO, he has a higher level of stringency and scruples to adhere to.
But then, there are a lot of Republican CEO's for publicly traded stock companies. Frankly there are also one's that attend campaign dinners and go to yacht clubs. I highly doubt that prevents people from working for them. In America, workers are focused on the task at hand, CEO's don't have any care (to judge against) the private lives of their own talent.
If you are reading this and are this or that - don't be dissuaded from working for a corporation just because the CEO's political beliefs. People are blowing this totally out of proportion.
Unless you're directly in contact with the CEO and he's spewing hate (rare) you are ok.
(I upvoted you.)