Dude, I'm not going to speculate on the device used by someone to write a wall of badly structured text to justify their own bigotry and mask it in in terms of faux psychology.
If you really want me to take that post seriously then I'll do so as a mental health professional, not a sci fi fan. If she really is attaching herself to a fictional character to the point she feels some imagined family dynamic has been disrupted and thus had a knock on effect on her as a child of that family then the question is not "who should be the next doctor", it should be how best she should seek out help for her issues.
The BBC makes shows to educate and entertain, it's in their charter. Doctor Who does both. They do not take responsibility for the mental health of an entire nation every time they make a casting choice.....
On the other hand it is possible the attachment issues with her "dad" stem more from the fact he seemingly fathered her with his own granddaughter, subsequently expected her to accept 20 plus attractive young women as "mum", developed a tendency to disappear for years at a time (fifteen on one occasion) and never settled in one place, literally calling a different planet "home" each week.
If after all that she still accepts him as a stable father figure I'm sure she can forgive a sex change on top.....