Ok. We'll try this. Without getting bogged down into a definition, let me see if you can provide an answer to a question. I'll try to avoid undefined terms by only talking about the cis/trans versions of the words. While some people don't like those words, I think we can at least agree on what they mean.
So, there is a cisgender woman. She wants to go swimming, but there is no private place to take off her clothes to change into a swimsuit, but she is willing to undress in front of other cisgender women. She is not willing to undress in front of cisgender men.
Now, suppose there is a physically untransitioned transgender woman. i.e. This person has functional male reproductive organs, but identifies as a woman. The cisgender woman says that she does not want to undress in front of that transgender woman, and believes that the transgender woman should be excluded from the locker room that the cisgender woman is using.
Can you provide a reason that the cisgender woman should be supported in her desire to exclude cisgender men from from the changing area she is using, but she should not be supported in her desire to exclude transgender women from that locker room.
Keep in mind that we don't want to get bogged down in definitions, here, so your answer shouldn't depend on how a certain word is defined, unless it is a word where everyone agrees on the definition.
ETA: I'm not sure if it really matters, but just for context I want to make sure people understand my personal stance on locker room access. Transwomen who have undergone full surgical transition ("bottom surgery") should be allowed to use women's locker rooms. Transwomen who have undergone no physical transition should not be allowed in women's only spaces, as a general rule. (i.e., individual businesses should be free to enact different policies. Planet Fitness can make its own rules.) People who have undergone some transition? I honestly don't know enough about the process, but at some point they should be allowed. I just don't know enough to say exactly when that point is. My own personal opinion isn't really necessary to answer the question I posed, but it might provide some context for the question I'm asking, so I decide to include it.