Nothing to do with her being female or black or anything. She just not my favorite character. Am I not allowed to dislike a character?
Nobody is telling you to like her. Disliking a character is fine. What grates people's nerves (including mine) is you insisting on lobbing that ridiculous term at her that, by your own description above, doesn't hold any water. Maybe you didn't know this (and I'm not being sarcastic or anything), but a Mary Sue (and man, do I hate this term) has to:
Have no character flaws. Burnham has them. She gets called out on them. She suffers consequences because of them.
Never be seriously criticised by other "good" characters. Spock calls her out. Harshly. Others have done so, as well.
Never face consequences. Boy, does she face consequences. So do those around her.
Never make serious mistakes. She fucks up during her first episode and makes some pretty bad mistakes over the course of the seasons.
Never suffer humiliation. She does on Vulcan. Spock sniping at her in front of Cornwell or Stamets counts, too.
Never have to work hard to acquire skills. She spent about the same amount of time studying as everyone else.
Be more skilled than others for no reason. Nope. Moving on.
Warp those around her out of character. Doesn't. If anything, it took folks a good long while to get used to her. People don't treat her better than others, don't cut her more slack, don't ignore others to pay attention to her.
Be at the centre of everything, all the time, and have the universe bend backwards to accomodate her. Also not true. All of the focus characters have, at some point, used their skills to save the day.
Have almost everyone attracted to her, wanting to befriend her, wanting to adopt her. She got adopted by Amanda and Sarek, but other than that, she doesn't get any more attention that way than others.
There you go. Use this rough guideline.Maybe do the litmus test. Maybe don't. Keep on disliking her all you want, but please, if you want people off your back, quit it with that frankly ridiculous Mary Sue accusation. It's inaccurate and just causes the impression that you, like so many others, are using a meaningless insult to disparage a competent female character. If that is not your intention, just stay away from that term. Problem solved. Thank you.
Moving on.