I am a VA resident and a transgender man. I moved here when I was 10, and publicly came out as trans at 15. I experienced the school system as a transgender teenager.

When I was in school, accommodations were made for me to be able to change in the changing room that was gender affirming for me, the boy's team locker room. I found it highly frustrating and unfair that similar accommodations were not made for my friend, who was a openly transgender girl. This directly contributed to substantial bullying from her being forced to share spaces with boys who openly mocked her and called her transphobic and homophobic slurs, even with a pretty trans-friendly staff, because a teacher cannot always be present to mitigate bigotry. It always seemed hypocritical that I was, and AFAB (assigned female at birth) person was easily given a safe and gender affirming space to change, and my friend could have no such accommodation simply because she was AMAB (assigned male at birth). 

Additionally, forcing trans women to use men's restrooms puts BOTH transgender and cisgender girls and women at risk. You may have an idea of "What a transgender person looks like", or even "what a cisgender person looks like", but the reality is human beings are multifaceted in all aspects of physical presentation. Inevitably, barring trans girls and women from restrooms and sports also reinforces sexist and patriarchal norms of presentation onto cis women.

Look at it this way: If it is an official rule or law that trans girls and women are barred from women's restrooms, it will create a vigilance amongst people both inside and outside the women's restrooms and locker rooms to 'catch' those who may be 'offending'. However, due to the natural variety of human features and how they are interpreted by our society (though, unfortunately, the norms of patriarchal sexism), it will place the target on 'women who have features and gender presentation considered masculine/unwomanly' as opposed to trans women exclusively, as many trans women are indistinguishable from people's cisnormative assumptions.

It's like how ocean trawling with huge nets is bad for the environment: Cisgender women who dare to be different from gender norms will become the bycatch and suffer greatly just for being themselves. Regardless of intention, the practical result of this sort of legislation is NOT protection of cisgender women, it is only the protection of cisgender women who fit ultimately narrow, sexist, and heteronormative conceptions of who a woman is and how she might look. 

Trans girls and women are in no way a threat to broader society, and banning them from women's restrooms will further stoke paranoia within those spaces that will lead to the harassment of cisgender women. This will also disproportionately effect women of color, who due to systemic racism are often already seen as outside feminine norms. 

To ban trans women and girls from public restrooms and locker rooms is to make an already extremely vulnerable group of people moreso, and invite further scrutiny and harassment upon other marginalized cisgender women who will suffer the brunt of paranoia, harassment, and humiliation as a result of the transphobic preconceptions held and accusations made by those persons who would be emboldened by this legislation to police who 'real' women are. 

Speaking from experience, I understand the importance of a sense of safety and refuge being present in women's bathrooms, and before transition I was supported many times by girls and women in that space. So too in that do I understand then, that transphobic people fixating on the birth sex of a person using the women's restroom and harassing someone if they find a 'misalignment' are much more harmful to the integrity of that space and the safety it provides than any trans girl or woman will ever be.