I'll do my best to summarize the situation, at least as well as I understand it.
When speaking in English, it often sounds awkward to repeatedly use the same proper noun in a sentence or paragraph. So, instead of repeated use of the actual noun, a pronoun is used.
When referring to individual people, or to some animals, the most common pronouns to use are "he" or "she", depending on the person being talked about. When referring to a group of people, the typical pronoun is "they". It's also possible to use "they" as a non-gendered pronoun for a single person.
By itself, the mere grammatical fact of these pronouns is not particularly interesting.
However, right now the United States, and other countries, are experiencing social and political tension around a broad range of related topics - how do we treat people of different genders? How do we treat people who are transgender? Or people who don't feel like they're clearly masculine or feminine? Should gender even have a great role in society?
Usage of pronouns has become a particular sticking point during this tension. For example, let's imagine a person named "Pat". Pat was born as a male, but wishes to be identified as a woman. When talking _about_ Pat, I have a few options in how I talk about he/she/them, and which I choose to use will divide me into one of two political camps.
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I could refer to Pat as "she", indicating that I respect her choice and identity, which also implies that I find her framework of gender at least tolerable or imaginable.
I could refer to Pat as "they", which is typically not particularly offensive, and some people prefer it. It shows that even if I don't agree with their choice, I want to sidestep awkwardness with them. This lightly shows me as being in the gender-inclusive camp.
I could refer to Pat continuously as "Pat". This would tend to sound awkward, and Pat might wonder why I won't use pronouns to talk about Pat, and might be mildly offended, but it shows I'm at least aware enough of Pat's feelings to try and avoid serious offense.
I could refer to Pat as "he", which would indicate that I do not respect his choice. Pat would likely feel that I don't respect him at all, and that I'm being belligerent in opposing his framework of gender.
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It seems like the inciting incident on StackOverflow in particular unfolded as follows:
* StackExchange began to introduce a new policy, intended to promote being inclusive of people of different genders and gender expressions.
* If I understand correctly, the policy indicated that writing should strive to be gender neutral. I believe in particular that this meant that the pronoun "they" should be preferred.
* One particular Moderator (by the username Cellio) of the site attempted to clarify, about whether writing that _avoided_ pronouns rather than using pronouns, would be allowed.
* _In Particular_, Cellio was concerned that the usage of the "they" pronoun to refer to individual people could be confusing to non-native English speakers, as "they" is more commonly used to refer to groups of people.
* Drama ensued, in which the stance of Cellio was cast as ideologically equivalent to the stance of someone who would intentionally use the wrong pronouns. (i.e., because Cellio was indicating that they did not wish to refer to a hypothetical Pat as "they", the assumption was that Cellio would refer to Pat as "he", even though Pat would prefer to be referred to by either "she" or "they")
* StackExchange thus fired the Cellio.
* Other people found this firing to be unfair, with a few reasons for finding it unfair:
People who agree with the ideological framework of gender which promotes inclusivity and sensitivity felt like the fired moderator was actually being quite reasonable, and that this was an over-reaction or misunderstanding.
People who don't agree with that ideological framework of gender see this as another example of an opposing political camp colonizing more spaces.
There are a handful of people who believe the firing was reasonable, but I don't believe I can adequately express their viewpoint.