After years of being simultaneously ignored and sensationalised, discussions about trans people and their issues have become mainstream. But the debate has sadly turned into a vicious fight about who should and shouldn’t have access to equality between supporters of trans and women’s rights – two groups that should have common cause.

In 2004, the Gender Recognition Act confirmed that transgender people exist, and their gender should be recognised in law. It’s a clunky process that relies on trans people demonstrating they have a mental illness. We moved on from labelling homosexuality as a mental illness back in 1992. Surely it’s long overdue for those who are transgender? As the prime minister reaffirmed last week at the Pink News awards: “Being trans is not an illness and should not be treated as such.”

Trans people and people who are neither male nor female should be recognised for who they are without abuse or discrimination; they should not have to go through a lengthy, degrading process. It’s notable that societies more conservative than ours – Argentina, Ireland and Malta – have all done it. Why can’t we?

Some believe that if people could self-declare their gender without the bureaucracy and paperwork, men will simply say “I am a woman” in order to access female-only spaces to abuse women. We all should be concerned about male violence, and we should all be concerned about preventing it and responding to it when it happens.

But granting trans people equality will not make women any less safe. We live in a society where, unfortunately, women’s safety isn’t guaranteed. But trans people are not to blame for this, and often they are at risk themselves. They cannot be made the scapegoats, or the distraction from the real issue. Granting them rights does not give violent men permission to be violent. The reality is that if a man wants to dress up as a woman to access women-only spaces, he’ll do it anyway. No piece of paper will prevent it.

Violent men cannot announce they are women and automatically get moved to a women’s prison

Domestic violence agencies and the prison service have vast amounts of experience dealing sensitively with people from a range of backgrounds. Domestic violence and rape crisis centres are concerned primarily with supporting the victims of male violence, and they will always find an appropriate service for anybody who arrives at their door, including trans men and women. They have been doing it for years without asking trans people to show their certificate. They know how to balance the complex needs with sensitivity and professionalism, although it’s clear that trans (and LGB) people require more direct services designed for them, such as the specialist LGBT service that sits alongside a women’s aid centre in Birmingham.

Prisons have also been navigating these issues for years. As the Ministry of Justice says in its own guidance, “allowing transgender offenders to experience the system in the gender in which they identify will, in the great majority of cases, represent the most humane and safest way to act. We believe it will also assist successful rehabilitation.”

When an offender indicates their intention to transition while in prison, they will receive central specialised support and undergo comprehensive risk assessment. They will be able to live in that gender regardless of where they are placed, but that doesn’t necessarily mean they will automatically be moved to another prison. Violent men cannot announce they are women and automatically get moved to a women’s prison. It doesn’t happen now. The system does not, and will not, facilitate a mass transfer of male prisoners into women’s prisons, despite headlines that suggest otherwise.

The tragic deaths of trans women held in male prisons shows us there is more to do to secure the safety of trans prisoners, but those issues won’t be resolved or made worse by changing the administration around gender recognition certificates. Increased awareness might, however, lead to better conversations, better care, better rehabilitation and fewer unnecessary deaths.

Trans people face the same risks to their safety as women. Research shows that 44% of trans people avoid certain streets because they don’t feel safe, and in the past year alone, two in five trans people have experienced a hate crime because of their gender identity. If that sounds familiar to any woman reading this, it’s because you have common cause.

Women and trans people both exist in a world where they are prevented from accessing true equality because of their gender. We must not be divided by arguments that undermine the equality we so desperately need and deserve.

• Ruth Hunt is the chief executive of Stonewall