I find the concept of people being against "fan service" to be somewhat bizarre. I think you put it well, "How dare they put in Star Trek in my Star Trek!" Like... that's why i'm watching this. I want my Star Trek to have Star Trek stuff in it.
"Fan service" seems to be... a production... giving fans... things they want to see. Why is this bad?!
I guess it's subjective. How much you put in, when, how obvious it is,
which things you include and where, the proportion, whether it helps or hinders the story you put it in.
You may love a particular food like chocolate, but not in everything you eat, smell, wear, etc. has to have chocolate in it. You may love dogs, but if every gift people buy you is dog-themed, eventually, you want something else.
At some point, you want to be surprised by new things, find different things to also like, different places to explore that don't all look the same, try something else for a change, even if you go back to the old thing again sometimes. If nothing else, you appreciate what you get a break from.
It's the whole idea of
Star Trek - going to new places and finding both old
and new things.