I don’t think thattranspeople should be denied rights because a minority of people will seek to exploit a new process.
That is the wrong framing. The question is not Should a vulnerable group of people be denied rights, because members of this and other groups may seek to exploit these rights?, it actually is Should one vulnerable group of people have their rights in law removed for the benefit of a different group of vulnerable people?
His framing allows your MP to pretend that there are no conflicting rights, but only a lack of rights for a vulnerable group for which the remedy has no effect on anyone else.
In reality, the situation is this:
Both groups, as well as several others are protected under the Equality Act. Situations where their rights conflict are carefully explored amongst over a thousand explanatory notes issued alongside the law which explain how it works.
Through the Equality Act, UK law recognises that female people are discriminated against on the basis of their sex. It gives them the legal right to define themselves in a category of their own, separately from males and allows for female-only legal set asides such as refuges, dormitories, sports and scholarships etc as well as the right to ask for a female nurse or carer or rape crisis counsellor and furthermore it gives them the right to organise and assemble outwith the presence of males to (amongst other things) advocate for their rights as a sex.
Ask your MP if he seeks to abolish this right.
If he does not, then you expect him to listen to your concerns about how self-ID will impact on our sex-based rights and to consider how the resulting conflict can be resolved without removing existing legal rights created through the protected characteristic of sex.
I would probably also want to know how he justifies treating as mere collateral damage the harm already inflicted on women and girls as a result of self-ID policies adopted in advance of the law reform. And how much more collateral damage he considers acceptable and how much he would consider too much.