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".
Again this is hyperbole and is not how people think. The politicization of everything and denying that some ideas are apolitical are tied. The latter is a false justification for the former.
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.
What is the current political climate? And is it static, will it not change?
Is providing food in supermarkets without political background checks "a political choice"? If so, then everything, including picking your nose with your left or right hand, is a political choice and the term "political choice" becomes utterly meaningless.
The current political climate is the policies enacted by politicians and the populace's reactions to it. It is not static, and it changes with the politicans in power, the laws in effect, and the political mood of the populace.
Then in your model of the world, how would one not take a political stance?
If everyone takes a political stance in your model by definition no matter what their intents or actions are then it's a rather useless definition.