Both sides are being pre-emptive. The EO basically opens up the possibility of people challenging state and federal laws in court, allowing transgender women competing on women's teams. One side doesn't ever want that to happen, the other side does. The emotional response is usually seen from parents of younger athletes - middle school, high school, etc...
Policy is clearly laid out for higher level compeition (NCAA, IOC, etc). The runway is much longer for these athletes - 4 years to identify as a female and monitoring testosterone levels for at least 12 months or so prior to a competition. I figure the testosterone thing follows roughly WADA guildelines for any banned substance.
I could care less what happens at the NCAA, Olympic, or pro sports level - have at it. They have common sense rules in place to level the playing field. I think there is room for concern at the middle and high school level. And yes, I know statistics show that it doesn't happen often. I've seen enough boys/girls scrimmages to know that once boys turn 14, height, weight, and speed matters. I've seen enough injuries at these types of scrimmages.