Well firstly I'd say there's a difference between having an issue with something and not like hearing yourself referred to as something. I had no issue with anyone.
Also it's context. Obviously saying things like "I wonder what made them do that" is a bit different as it's natural to say. This is more purposely avoiding "he" and "she" to use "them". No issue with it, but to my ear it strikes as rude and unfriendly. Wondered if anybody felt the same about it. I don't see why I keep getting replies like this.
I really struggle with the they/them pronouns.
For me it's a cultural thing and probably embedded with age.
Might be hard to understand but we (culture/nationality South Asian) have always used they/them in English from a very young age.
English not being my first language (as in didn't learn it first, it is the main language used), we have separate pronouns for elders and people we show "greater" respect to. So I would never refer to my mum or dad as he or she. It was always they or them. Similarly with a teacher or Imam/priest etc.
I used to get told off as a kid in school for saying stuff like "they told me" when having a conversation about say my mum to the teacher. In essence we used the plural for elders.
I briefly taught him a high school and even second Gen kids from my neck of the woods were using they/them for parents etc. I often explained to teachers that this wasn't a kid struggling with English but a respect thing.
Our language has specifics whereas English doesn't in many cases. So it's not just aunt and uncle for us. Dad's older brother is a different word meaning uncle, younger brother is different word meaning uncle. Mums brother is a totally different word meaning uncle and same for sisters.
When addressing my younger brother I would use "tuu" meaning you but older sister or parent/teacher/ grandparents etc it would be "tuusaan". This when using English makes the plural, if that makes sense?
For example, When relaying a message to a sibling from mum I wouldn't say "she said...". I would say "they said..."
If a younger Asian person came out as trans or wanted certain pronouns using nobody would use they/them for that person. Yet an older person would be they/them irregardless.
So from being told off from using they them as a kid now it's the other way around