What would be interesting would be a separation of biology but also an understanding.
I think a possible solution is to treat trans as separate category; while not completely fair there is some degree of culturally-accepted fairness possibly? Let me think it through... I don't know if it would really be fair to have trans people compete with men either because even though their birth sex assignment is male, they are still biologically different, especially after transition. I mean in reality sports are never really fair to begin with on the basis of biology. Using sex as a separator is just a generally socially accepted way of separating people, something that most people accept as a binary, something that is kind of mostly based on science but obviously there are outliers.
I think this is also where discussion of equality gets a little messy too, and because the concept of equality in the minds of human beings is not really clearly defined. Even though people want to treat men and women with equality, we still permit and celebrate a separation of sexes in sports. In general, men's averages are higher then female averages, and in almost all sports, men's records and elites are better than women's records and elites. Based on this, it seems more people would have a problem with a trans female competing in female sports than a trans male competing in male sports. I know there are also some rare situations in which a female wants to compete on the boys team, and while this is not universally allowed/accepted, people don't really see it as unfair.
Some high school athlete in an article about the high school wrestling trans male competing in female wrestling said that she felt they should be allowed to change their gender but wait until after high school or quit the sport altogether. My suggestion is maybe rather than quitting the sport altogether, create a new competition? Or maybe society just needs to come to an understanding that this is messy and just let people compete in whatever gender the contestant feels they are connected to (maybe it needs to get medically/psychologically verified though) and accept the "unfair" ramifications, even though some people are already born with much more dramatic biological differences to begin with.
Even though women have always competed in sports with men, the notion of separate women sports is also long in history. Women's sports and adaptive sports exist in part because on average, an elite woman and an elite adaptive performs worse than an elite male. Putting trans in adaptive sports wouldn't make sense, and putting all trans and intersex in their own collective category would not be fair to transmen/women who can compete on the same level of some elite females/males, just as Oscar Pistorious was allowed to compete with non-adaptive men. Also while it is accepted to put women in a different sport than men, it is not accepted for other biologically-related differences.
I don't really know where I was going with the last paragraph but basically there is no clear cut answer that really is fair to everyone. The main reason this is such an issue is putting those who were sex assigned male or intersex into female competitions and this is seen as unfair to those who have felt and been identified as biological women since birth. However, what these arguments also ignore are biological differences between women and how it is also basically accepted inequality to put women in a different category than men. Perhaps this is why, according to the third place finisher in the article, she just wants to focus on the clock - "'To be honest, I think it's great they get a chance to compete and as long as they're happy, I guess, there's not that much I can do,' she said. 'The rules are the rules. The only competition is the clock. You can only run as fast as you can.' "
So IMO, having trans as a separate category would only work if trans wanted that. If they didn't, oh well. It's not fair to them to not participate, but they should follow the same hormone rules and other rules as men and women to keep it fair as much as possible within those sports. The rules can always change, but the rules should not be changed to specifically exclude or discriminate against trans individuals, only those who try to compete unfairly. People also need to realize that sports are not fair to begin with and maybe they will care less.