The question isn't about whether the trans-identified have their basic rights. Of course they do, like every other citizen. It's about whether they should be granted extra rights, particularly those that override the existing rights of women.
For example, should a trans-identifying male criminal have the right to be incarcerated in women's prisons? Some female prisoners have already suffered rapes and sexual assaults from such males, in states that granted this right to the them.
It's another example of the balance of rights, just as privacy rights are.
Also, the feminist activists who are advocating for women's sex-based rights are largely anonymous or pseudo-anonymous due to potential repercussions from vindictive men who oppose them. Online privacy in particular is vital for their activist movement to proceed without intimidation. It works both ways.
For example, should a trans-identifying male criminal have the right to be incarcerated in women's prisons? Some female prisoners have already suffered rapes and sexual assaults from such males, in states that granted this right to the them.