I think a lot of people are missing the bigger picture here and are too zoomed in on the specific issue of unionisation. Google really had no choice here, and it's actually a problem for them that this is coming out now via a blog post by the fired employee and not by their own admission.
Google is in a phenomenally trusted position in the world. Chrome is the most popular browser. It auto updates silently and continuously, as do installed extensions. Vast swathes of information and infrastructure is accessed via web apps. We tend to forget that browser makers have access to all our authentication tokens and can do whatever they like.
Put simply, given the level of web dependence in our lives and infrastructure, those who can modify browsers are practically gods. The same goes for operating system developers of course.
We don't think about this because our level of trust in those developers and the corporations they work for is extremely high and deservedly so: after decades of using operating systems and web browsers they've never violated that trust. In fact they've reinforced it by rolling out encryption to block rogue government departments who were exploiting the lack of it, they've invested heavily in security to lock out hackers and done many other great things.
But trust is hard to build and easy to destroy. What if browser makers stopped being so trustworthy? What if they started to become convinced of their own superior morality, the correctness of their political judgements, the importance of their role in the world? What could they do?
They could use SafeBrowsing to arbitrarily censor the web.
They could edit out individual comments, rewrite news stories, insert their own views into the middle of documents purporting to be neutral. They could distort your view of the web at will.
They could violate our privacy at will by linking our identities together and then publishing what we've written, they could publish browsing logs, they could take over any accounts we have and use them for whatever purposes they like, they could feed sensitive information to political enemies to give themselves plausible deniability, they could even frame us by posting illegal material under those accounts. It'd just look like someone phished the password.
They could do many other things we never even considered.
Google absolutely needed to go nuclear on this employee. The news has been filled over the past years with stories about Googler's increasingly hard-left political activism. As a consequence some users and even politicians have started to wonder if Google Search is trustworthy, but their trust in browser developers is so total, so blind, the world hasn't yet taken the next mental leap and started to wonder if Chrome is. Mozilla is hardly in a better position: it's funded by Google and literally just down the road from them. If the integrity of the Chrome devs start to be doubted, few will consider Mozilla devs to be radically different.
Inserting political JavaScript via browser security mechanisms targeted at Googlers, even if it may seem fairly harmless in this case, is a very problematic situation and a slippery slope Google simply cannot afford to go near. It raises fundamental questions, like are Google's internal procedures robust? What else might have been slipped through code review already? Are Google employees only adjusting their own tools or did some already start to abuse their access to people's private data and systems? How many of them feel the ends justify the means when dealing with political causes they feel passionately about?
How safe is Chrome, really?