If you have a more genderist MP you can still lobby but if you want to be more subtle try to get them to vote for Preet not because she believes women are real [I wouldn't necessarily mention that], but because her background and experience makes her best suited to the role because she has way more experience of ordinary life and vital skills.
She comes from a working class Sikh background. Her father was a foreman, and later a bus driver, and her mother worked as a seamstress and Preet attended a comprehensive, then the University of East London. She is the first female British Sikh MP elected to the House of Commons.
Preet was a social worker in Waltham Forest and Birmingham specialising in child protection and serving as children's services manager in Birmingham from 2010 to 2017. So she has worked right at the sharp end in very difficult conditions.
In contrast :
Olivia Blake's mother is Judith Blake, Baroness Blake of Leeds CBE , a professional local Labour politician, former Leeds city council leader, appointed a Lord in 2021 and originally a teacher. Olivia Blake attended a Grammar school, and Sheffield University and is very middle class. She has followed a political career since leaving university and has little life experience.
Dame Anneliese Jane Dodds DBE had a Chartered accountant father, she attended private school and then went to Oxford University, her master's degree in Social Policy at the University of Edinburgh, and a PhD degree in government at the London School of Economics. She was a lecturer before getting involved in Politics as an MEP. Dodds has a powerful resume and much academic knowledge, but the chair of the committee requires someone with way more hands on experience.
Even if MPs vote against Preet because she believes in women, make them feel guilty about selecting more privileged women over her. Imply they are being racist and classist. Which they probably are to be frank.