I wouldn't as well, but as soon as that developer would become representative of my company and people would start to bring it out in connection to the company, I'd start to worry about my image.

For your typical standard worker it doesn't really matter what he/she does outside of work, as long as it doesn't damage the company - which is pretty hard unless you really try, since nobody outside gives a damn about some noname employee. For someone very high in hierarchy it actually becomes much easier to damage it, so you have to draw a line somewhere. If your company, supposed to promote messages of equality and taking pride of its supposed openness, elects someone who actively supported means of oppression against minorities as its representative and people start to react, there might be something worth reconsidering in this situation.