I don't think the majority of police officers are misogynists. They are, however, drawn from the same society as the rest of us, where many sexist and misogynistic attitudes are culturally ingrained even in our Western, largely progressive society. It's therefore no surprise that the law, which in the main has been written by men, doesn't protect women as it should. It's not so much that the police are institutionally sexist as it is that society is institutionally sexist and the police simply reflect that.
Britain is generally a liberal and tolerant country. As equality and diversity issues have become greater understood and we've recognised what we're losing out on by not being inclusive, publicly funded bodies are rightly seeking to make changes. The trouble is that they're monoliths and funding for these issues is minimal. Therefore, senior leaders understandably look to the easiest solutions. Stonewall provided them with one in a way that women's rights groups have never been able to. Stonewall provided a single ideological strand with practical solutions and template workplace policies. No wonder it was seen as an easy route to demonstrating a commitment to diversity. Women's rights, however, doesn't have that cohesion - there is significant disagreement between feminists on certain subject matters and there are no 'insert name here' easy-to-implement policies. Most bodies have tried to progress women's rights through a collective of different and disparate initiatives drawn from different sources. Therefore it never achieves the same momentum as something like Stonewall.
There's also the small matter that because women make up 51% of the population and increasingly significant proprtions of the workforce, any real change is going to be expensive and demand significant effort, some of which may prove controversial and difficult. Most bosses continue to see the LGBTQ+ issues as somewhat niche, unlikely to impact on many people and therefore an easy win. Hence it gets pushed through quickly. Changing signs to gender neutral is a whole lot easier than building more disabled loos or rewriting your maternity leave policy for example.
I don't think the police (or any other public body) will change their current stance until they are either provided with evidence that they are losing public confidence because of their approach, or they are legally challenged on their impartiality and public sector equality duty to encourage good relations between different groups. Another legal challenge may be that they are supposed to record legally defined protected characteristics not gender identity. It would be interesting to see what happens in that case, but I'm sure the original intention was meant to be one of inclusivity rather than a deliberate attempt to obfuscate data. It could be argued they should have seen that coming, but again that comes down to most people initially believing *and in many cases still believing) this was a very niche issue which would have little impact.
Many police forces spend significant sums and training on tackling child sexual exploitation, rape, domestic abuse. Most officers genuinely want to tackle it. An increasing number of officers are rightly being dismissed because of poor behaviour towards women because the police are getting better. However, the reason progress is limited IMO is because what's really lacking is a feminist analysis of how society creates the opportunity for these crimes to arise in the first place. Applying that might mean shining a spotlight on our society and its ingrained sexism that governments of all colours might not yet be ready to acknowledge and tackle in any meaningful way though...