@Lampy123678
Are you saying when you see the word people you read men?
"People" means women and men, as you know. Men are not the target, no man has a cervix, so why include them in the messaging? It blurs the message that this is sex-specific healthcare.
No woman/girl of cervical screening programme age will not know she is a woman. Even if she has a DSD, she will know she is female.
Every woman who claims to be a man, or to be neither a man nor a woman, knows she is actually a woman. Of all women, they are the most likely to know that they have a cervix.
Of course this healthcare is unique to women. If they want to add something like - this information applies to non-binary females and transmen, fine. But you can't pretend that those women are not women, in a healthcare setting. It's dangerous to encourage the delusion and harms women generally to talk as if having a cervix is just some random physical feature.
But ultimately as I said before, calling women "people with a cervix" has got nothing to do with reaching women with special identities. If it was, there would routinely be equivalent language in testicular and prostate cancer awareness campaigns to refer to men who claim to be women.