Again, because you are not surrendering any rights, privacy, safety, or dignity to us. I'm sorry you feel that way, but it is just not true.
Transpeople gaining rights doesn't take them away from you, no matter how much you think we are.
I don't see how you can say it is objectively true or objectively false.
You could argue safety objectively, by citing statistics about reported victimization with or without transgender access.
"Rights", is a philosophical concept too deep to get into here.
"Dignity" is very subjective.
But, privacy?
Would you agree that if I, a cis-male, went into the women's locker room at Planet Fitness that I would be invading the privacy of the women in that locker room? I think the answer is yes, don't you? I'm going to assume that's the answer.
And I think that if a cis-woman goes into the women's locker room and uses it in the normal fashion, she is not invading the privacy of the other women in the locker room, and I assume you agree.
So now, we differ on whether a trans-woman entering that space is or is not invading the privacy of the women in the locker room. Is the trans woman more like the cis-woman, or more like the cis-man.
I don't have an objective answer to that question, or to the underlying question that caused me to ask it? I can't define "more like". You say she is not surrendering any privacy, but how can you say that objectively? if you accept the concept of invasion of privacy, and agree that a cis-man would be invading the privacy, how can you say, other than by bare assertion, that a trans-woman is not invading the privacy of the women.
You might say that I am doing exactly the same thing, by asserting that the trans-woman is invading the women's privacy, and I can't argue that you are objectively wrong. However, I can say two things about the situation. My subjective evaluation that her privacy is being invaded is based on the theory that a man watching a woman undress is invading her privacy. In order to decide whether a given individual is invading her privacy, then, it is sufficient to show that the individual is a man. In order to do that, I have to have a definition of "man". As it turns out, I do have a definition of "man", and by that definition, a trans-woman is a man. is there some alternative definition that would make the transwoman not a man?
We've been over this before, of course, dozens of times in this thread and its predecessors. All the proposed definitions are circular. The closest anyone ever came was saying that "woman" was anyone who filled society's female gender role. Depending on how deep you dive into it, that is either a circular definition, and therefore meaningless, or it is an assertion that "man" or "woman" is defined based entirely on some combination of individual behavior plus societal expectations of behavior, which is a proposition I don't think anyone will defend.
The second comment I will have is that while I cannot objectively state that privacy is being invaded without some degree of bare assertion, what I will say is that as long as the majority of women feel like their privacy is being invaded, then their privacy is being invaded. It's subjective, based on the feelings of the women, but if I cannot come up with an objective definition of "invasion of privacy", I can still say that I will consider it having occurred as long as the expectations of privacy are being violated, and in the case of transwomen in the locker rooms, they clearly are, at least until expectations are modified.