A few days ago, David Challenor, the father of a high-profile Green party member, Aimee Challenor, was convicted and sentenced to 22 years in prison for child rape, torture and other depraved and horrific crimes. My thoughts are with the survivors of his shocking and disgusting acts.

The Green party has, rightly, faced questions about its association with David Challenor, who in the past has acted as an election agent for his daughter and whose own membership of the party has now been terminated with immediate effect. Our governance bodies have established an urgent and independent formal investigation and a review of the party’s safeguarding and child protection procedures, and Aimee has stepped back from her spokesperson role, as well as withdrawing as a candidate in our current leadership elections.

I have faced many calls for immediate action against Aimee – calls that fail to understand the very limited powers I have as a party co-leader and that assume I would be prepared to ditch the fundamental right to due process and a fair hearing. Justice and truth must not be further victims of David Challenor’s crimes and nor must trans people’s rights.

That Aimee Challenor is a trans woman should not be relevant here yet others have tried to make a connection. While we can all agree that what her father did was monstrous, the transphobia unleashed against her on social media is absolutely unacceptable. So too is the aggressive and regressive vilification of those wanting to discuss trans issues. There have been bomb threats and bots systematically blocking women on social media to try to silence those who are asking whether trans rights put women’s rights at risk. If we want a more equal society we need to talk about how to get there. The positive response to high-profile celebrities like Caitlyn Jenner has done little to change the fact that trans people experience high rates of suicide, poverty and persecution. Rather than name-calling and accusations of bullying, tackling the routine exclusion and discrimination trans people face requires listening and learning.

My party has long recognised that trans women are women and trans men are men. That’s been upheld by the law since 2004 and gender dysphoria is a widely recognised medical condition. I, like many others, have faced my own journey when it comes to understanding a new way of thinking about gender – one that’s resulted in understanding how the idea of gender that’s underpinned my lifelong feminism is very different to what it means and how it feels to be a trans person. For example, I personally still find it very challenging that there is often so much focus on body parts, when a fundamental tenet of my feminism has been that gender is a construct independent of vagina and ovaries.

I don’t have the answers to all the difficult questions that are being asked. What I do have is a firm commitment to looking at the facts rather than being swayed by fear and speculation. Take one example: despite what you might read elsewhere, there’s no evidence that allowing trans people to self-declare will open doors for predators intent on abusing or attacking women and girls. Rather, obtaining a gender recognition certificate (GRC) will not change anything much other than removing the obstacles for trans people wanting, for example, an amended birth certificate or driving licence. It does not in any way affect whether a person presents as a man or woman on a daily basis.

If an individual wants to present as a different gender to the one they were assigned at birth, they do not need to go through the self-declaration process to do so. In many of the instances about which there are concerns – for example, women-only spaces being abused – self-declaration will make no difference. Women are not asked to prove their gender when they access refuges or other domestic violence support services, and trans women are already able to access these spaces without any documentation whatsoever. Anyone seeking to cause harm to women can already also try to access these spaces or services, which are in turn entitled to take action if they think a user or potential user poses a risk to others.

I’ve not seen any evidence that self-declaration has been routinely abused to gain illegitimate access to women-only spaces in any of the countries where self-declaration already exists. Nor is the theoretical possibility that individuals might undergo gender reassignment for abusive purposes a good basis for law-making. It’s also worth noting that a GRC is a legal document, and results in someone’s details being formally recorded. Anyone seeking to cause abuse would be drawing attention to themselves by using that route, and it’s far more likely that most people with illegal intentions will seek to operate under the radar.

I understand people’s fears, but they must not be used to justify the demonisation of trans people or the denial of their rights, nor as an opportunity to claim that women’s rights are at risk from trans equality. It also detracts from the important work of dismantling our patriarchal social structures. Of creating a society in which we are all truly equal, free and empowered to choose how we live our lives – including the right to choose a different gender to the one assigned at birth and to live free from any gender construct imposed by society.

We are living through a time of huge change in our understanding of the way gender works and the way it can be used to oppress others. We will survive not by turning on one another but by defending the right to free speech, protecting against hate crimes, finding a way through the current debate about trans rights that’s respectful of one another and the facts, and refusing to engage in violence and abuse. We will survive by focusing on our shared objective – for all women, whether cis, trans, lesbian, disabled or women of colour, to feel safe.

I’m sure I’ve not got everything right, but I believe what matters most is being committed to continuing to learn. Publishing this piece may well bring down anger upon my head and I have thought long and hard about whether to do it. What helped me decide is knowing that unless we’re prepared to listen to each other, and to debate the way forward honestly and respectfully, we’ll never make progress towards the future I believe is possible. I will continue to do all I can to ensure the Green party plays a constructive role and learns the lessons it needs to.

• Caroline Lucas is co-leader of the Green party of England and Wales, and the MP for Brighton Pavilion