The greatest upset at the 'only women have a cervix' is from men who identify as women because it doesn't follow the mantra of 'Transwomen are women'.
Though Stonewall have only just realised that their campaign to allow people to change their sex marker record on the NHS causes real problems
"only women have a cervix" says nothing about women or transwomen who do not have a cervix. If transwomen take offence at it they are taking offence at imagined slights. If they believe "transwomen are women" in a biological sense that is clearly incorrect - as you say it is a mantra and can't be generally accepted without full explanation, discussion and agreement on what that means - something that can't happen on twitter.
Also, worth distinguishing between transwomen and trans-activists - as they are not the same groups. I suspect that trans-activists, for various reasons, manufacture outrage at statements that most transwomen/men would not object to.