Again, personally I tend to fall on the side of the government having less ability to restrict speech but it doesn't really bother me if companies want to restrict the kind of speech their employees can engage in at work, or what kind of speech they'll allow on their platforms. This gets trickier in cases where the companies might have businesses that approach what I would consider a utility, but that's a different topic, and really that has more to do with regulating companies as utilities.
I'm not positive in this, but I do suspect that if stories like the one you linked found themselves on the front page for hours at a time, perhaps if some Googlers tried to unionize and they were all fired, we would probably see quite a few people be defensive of their right to speech. I doubt we would see a complete overlap, but it wouldn't surprise me at all if we would see some overlap in the posters defending their speech rights with those defending the speech rights of neo-Nazis. I suspect we might also see some posters who think all Nazi speech should be outlawed but think this kind of unionization related speech should be protected.
You're of course correct that these topics do tend to bring out the trolls, but on a site like HN I tend to find it relatively easy to identify trolls, even if not through a specific post they make, a quick glance through their posting history often reveals whether they are engaging with the community in good faith.