I would absolutely take that position. How is it relevant to his position? Can't someone pragmatically act as is appropriate to the world that is, while working to remake it as they believe it should be?
If Mozilla appointed, say, a KKK Grand Wizard to the post of CEO, that would definitely be relevant. First, because every non-white person would immediately have rational cause to fear discrimination. Second, because every anti-racist employee, partner, and donor would have incentive to reevaluate their willingness to help Mozilla along. And third, it would be an enormous PR nightmare, an unending distraction from Mozilla's actual work.
All companies are human institutions. And nonprofits basically all make a deal with their employees: You may not get paid as much, but you'll be doing something you believe in. It's immensely powerful, but it does mean you have to keep it a place that people can believe in.
There's a big difference between donating $1000 to a legal political cause and being a leader in an organization known for violent and illegal activity. If someone donated $1000 to the Freedom From Religion Foundation's legal fund, would that mean they could not be the CEO of a non-profit organization that might employ religious people?
Regarding the FFR, I'd say no, because as far as I know they aren't trying to strip a civil right from somebody. But suppose we were in one of the eras of American history where Catholics were seen as deeply suspicious by Protestants. If a protestant CEO had helped strip Catholics of, say, civil recognition of Catholic marriages, then yes, I would say that Catholics could be reasonably concerned about working for him. Even if he pinkie-swore to keep his anti-papist rants entirely out of the office.