We don't really know yet how his personal beliefs will affect the company. Read through some of the other comments here, I agree it could just be in very subtle -- yet still negative -- ways.
What I think is more interesting is how this reveals how deeply rooted sexism and homophobia are in our society. Yes, racism is still obviously a problem, but think for a moment what the reactions would be if the new CEO was known to have donated to KKK.
Here are some more fun exercises:
* what if the new CEO was a scientologist?
* what if the new CEO was an African American and it was revealed he donated to a group that attempts to make interracial marriage illegal again because he believes white people are sub-human creatures (the way the actual new CEO probably sees gay people, since he doesn't believe they deserve human and civil rights)?
* what if the new CEO was a neo-nazi sympathizer?
* what if the new CEO was a woman who really, really doesn't like men (and maybe even donated to some cause that attacks men or men's rights in some way)?
You can argue that all of these are just opinions. But where do we draw the line? People are usually very inconsistent with that. Homophobia is tolerated while putting a woman in a leading position makes people question this decision. Heck, people get all riled up over Ben Affleck being the next Batman, but the fact Bill Murray abused his wife doesn't stop him from being a geek idol.