First of all, everyone who insults Semenya by calling her a man, or "disgusting", or mocks her for her sexuality, which she clearly didn't chose, doesn't just act childishly (or worse), they also perpetuate the sentiment amongst many that hers is a gender rights or LGBT rights issue, and that a sport who wouldn't let her compete is backwards, homophobic, or both.
Also, sports is inherently about "advantageous genes", so if Semenya is to be disqualified from competing against women, the argument has to be a bit more sophisticated. If she was the only elite runner, it would be hard to argue that her extremely high testosterone levels are the main factors for her athletic success - after all, at the top end of any reasonably popular sport, you are bound to find genetic outliers. Many top basketball players are extremely tall - and yet, a 7'6" player gets applauded, not disqualified, despite his obvious genetic advantage over a 5'10" player.
However, the appearance of Dutee Chand and other hyperandrogenic athletes alongside Semenya (and a litany of doping cases) does indicate that there is a particular advantage to having very high testosterone levels, to the point where it distorts the competition. The question then becomes whether they are simply the 5-sigma outliers in a continuous distribution, or if there is some clear discontinuity that would allow one to draw a sharp line and establish a better distinction between two categories of athletes. After all, for every 7'6" player, there are several 7'4" players, and many 7'3" players that can compete fairly. Is that true when it comes to androgenic females? These are the questions that should be answered, but as long as both sides make this a fight about gender identity, it's not going to get us anywhere.
Clearly, the fact that sport has for centuries been divided into "male" and "female" doesn't help, when people start questioning Semenya's gender because of her testosterone levels. There is no question that she is female, the question has to be whether there should be some different set of biological criteria that can more fairly discriminate between two bimodal distributions.