Political neutrality is just political support of the status quo. That is a perfectly acceptable political stance to take, but you should recognize it is still a political stance.
Neutrality is different than support for the status quo. The status quo actually requires constant political activity to maintain. It's changed dramatically in the past decade. To support the status quo you would have had to restrict politics to e.g. Hillary Clinton on one side Marco Rubio on the other. You might consider that "neutrality" but I think what GP meant was rather that they prefer colleagues and management not to talk politics at all.
Granted, most people say political neutrality and they mean a homeostasis for what they like, but some people can say the word and mean it -- such as a YouTube platform that really just doesn't look at what gets posted.
Imagine you are a parent of two children, one 10 years old and the other 7. The two children are fighting with each other. What is the result of staying neutral in that argument? If you don't intervene the 10 year old is almost certainly going to win because they are likely stronger and more mature. By not intervening you are tacitly endorsing the 10 year old's power of the 7 year old.
The same thing applies in any fight/conflict/argument/debate when there is a power imbalance including in politics. This is most obvious in debates about civil rights. When it comes to those issues if you don't support an oppressed people you are endorsing the continue oppression of that people.
So you disagree with the actual definition of a word? This is absolute nonsense. From a legal and a linguistic perspective, neutrality is well defined. Sometimes people just don’t want to hear your crap, and the particular flavour of crap is of no relevance. Sometimes people just do not wish to be disturbed. It’s not a power struggle, it’s basic human decency. It’s understanding that you don’t necessarily know what other people at work are going through, and it’s also none of your business.