A non-political stance would be one which has zero side effects on anybody other than yourself. As soon as the actions you make and the decisions you take have an effect on somebody who isn't you, it becomes political.
Actually _taking_ a non-political stance is an exercise left to the reader.
Indeed! We all take political stances every day and it is certainly not possible to run an apolitical social network. The word is probably not very useful. But being able to reflect on “sensitive” issues is extremely useful and, I would argue, necessary.
And yet any random person on the street can easily flag something as being political or not political. I don’t accept that everything is automatically political. That is just an unrealistic argument that doesn’t match the reality of how the word is used.
You're correct. Almost everyone can efficiently categorize things they disagree with as "politics", while categorizing things they agree with as "common sense".
Taking that logic at face value, it would mean "if you choose not to take a political stance, then you still have made a choice". Okay, so you've chosen not to make a decision. Yet I don't see how having made the choice implies you've still made a decision ("you have still taken a political stance"). If anything it seems like you just argued against the point?
Choosing not to restrict what political things people can say (or to whom) is definitely a political choice. In many contexts today in 2020, choosing to allow others to speak about their opinions without restriction or opposition is seen as, not only a political choice, but an active attack.