Is it really a case of wanting to silence those views? To me it looks more like PR. "We don't associate with people with bad opinions, so we're good".

I would even go so far as to say that "companies" don't really care. The reason being is that for firing someone, you must have hired them first. But they consider there's something to gain, image-wise, by taking this kind of stand. This, they hope, can be transfered to dollars, so it looks like a good strategy.