Would it make you feel any better that he's already being accused of being a transphobe for one of the Executive Orders he's signed already?
He is not being accused of being a transphobe. Women's rights advocates are upset with him because he basically signed an executive order that would do away with any kind of gender discrimination. The wording of the order would imply that trans people could not be preventing from competing in female events. The wording also suggests that biological men could not be legally banned from areas designated as female only, like locker rooms. There could be no such thing as publicly funded female scholarships. Basically, many of the exclusively female benefits would go away, as would protections.
The transgender population is roughly 1%. I am not counting people that say they are "non-binary" or "gender fluid" because those are just people looking for attention. I speak of those that genuinely seek to be viewed as a gender opposite their own. In fact, the whole idea of transgender would imply gender is biological and binary. If there were infinite genders, and gender was based on how you feel, there could be no transgender people.... but whatever, back on topic. For 1% of the population, Biden just eliminated a lot of what women's rights groups fought to obtain.
The funny thing is, by being against the inclusion of biological males, women are admitting that they are not as strong as men and that there is a biological difference in physicality. I do fear for women's safety, not from genuinely transgender people, but from creepy people that will use this order as an excuse to invade female communal changing areas. This is one of those things that shouldn't have a law, but we should be able to use common sense for.