I have no problem with men who truly believe that they should have been born female and who truly do live, act and react as though they are women (or vice versa). That includes the majority, who live blameless lives among us, stay out of the controversies engineered by Stonewall, and are not being well served by the aggressive tactics of some activists. There have been individuals who lived like this throughout history.
I do have a problem with men who are still male in body, hormone production, heterosexual orientation and physical sexual reactions to the sight of women's bodies, but who, if this legislation goes through as it is planned, will be eligible to enter the communal changing room of a women's clothes shop and watch "other women" taking off their clothes without the other women being able to object because the trans woman is a woman too . Trans activists say that a lesbian could do the same, but that is like saying "There are man-eating sharks in the sea, so we shouldn't be worrying about dumping all our waste into it, even if some of it is poisonous and will kill wildlife"
I have a problem with violence to women by trans women being recorded as a female crime, when in fact it is by "a man who self-identifies as a woman but who still has male equipment and/or hormones and carries the same propensity for anti-woman violence as he had before he self-identified" thus skewing the statistics.
I have a problem (having had difficulties enough researching my family history, even without this complication) with people who have transitioned being able to completely obliterate the fact that they were registered in one sex and appear in later records and certificates as another. This could also cause problems if a person is being traced for some legal reason, or because they have done something that was not legal. I would hope that some kind of "audit trail" is left to indicate what was, after all, registered as a legal fact before the individual transitioned.
I am not happy, either, with the eagerness of gender therapy experts to prescribe puberty-delaying drugs, or hormone-stimulating drugs which are intended for people whose natural hormones haven't got into action by their mid-teens, not for prepubertal children. Once children are set on a course of action that includes such medication, they are almost certain to stay on that course into adulthood, even though their natural development into fully sexual adults may have made them perfect content (or very happy!) as their natal sex. Disillusioned and detransitioned adults are on record as regretting their sterility as a result of pubertal delaying drugs, or their unreversible body surgery.
These effects of transition need to be addressed before legislation on the subject is set into law and difficult to alter.