Labadabbado
What you say doesn’t make sense. Men were in bathrooms/changing rooms with boys throughout the last century. Some of those men would have been gay, most not. A small proportion of those men would have been paedophiles.
Some boys in those bathrooms, and some outside them, and boys in boarding schools, and boys in sports, boys in churches, or childrens homes were molested by paedophiles - men attracted to boys so gay.
Pearl clutching or not it sometimes happened and continues to happen. Pearl clutching is irrelevant.
Women don’t want to share private spaces with men. A few men are dangerous for women and girls. Many men hassle women and girls. A transwoman is no different - all it takes to be considered a transwoman is to change into female clothes, relatively few undergo surgery.
The equalities act says that in certain circumstances women have the right to separate sex based spaces, and rightly so.
Apart from this, unlike being gay, affirming a trans status with gender dysphoric children to soon, giving them puberty blockers, cross hormones and surgery could cause them terrible harm. Being gay will never cause such harm.