These two things are entirely mostly unrelated. People who do not want to be misgendered for whatever reason use them to avoid being misgendered as often as possible. To be inclusive some allies include theirs also, it shows some level of support and helps normalize displaying pronouns. You can still support others without putting your own pronouns promenantly out there for everyone to see.
Take me for instance. I identify agenderly but use he/him pronouns mostly becuase that's how I was born and look. I, much like you, don't care about how I'm pronouned, and honestly I prefer however I'm presenting at the time. In life it doesn't change much. But in games it can vary.
My own opinion on pronouns being that they exist to ease conversation, and so long as they do that, I have no problem using anyone's preferred selection. Up until someone decides their pronouns are so unique that it's not really a pronoun anymore, it's more like a second name. That's when I get a bit petty and will generally avoid talking about whoever that is at all.