Off the top of my head, I think the reason misogyny is harder to implement as a potential hate crime is the current political narrative that males can sometimes become women. If we didn’t have that belief floating around in the political and social aether then I firmly believe it would be easier to attempt to frame legislation around punishing misogyny.
But as things currently stand legally, allowing males to obtain a legal sex of woman means the law is inadequate to the task of defining what women are, in and of themselves, as a category. Therefore, it seems to me that if the law can’t adequately define a category of persons (in this case women), any politicians adopting the existing legal definition/consensus (based both on the law and any previous precedent-setting legal decisions) can’t adequately draft legislation to protect that particular category of persons.
We need to ring fence the definition of woman to apply only to adult human females before we can attempt to frame an anti-misogyny law that wouldn’t also allow men to use gender ideology-related definitions of woman as a defence against charges of misogyny made against them or to use the anti-misogyny law to punish women for being 'misogynistic' towards them.
Another consideration that’s occurred to me is that genderists in all administrations of the UK, both devolved and at Westminster, are very keen to create an opportunity to define women in any law they can, This is in order to have a gender identity-friendly definition (that includes males) appearing on the statute books somewhere as a basis to be built on in the future. And I think they would push hard to use any new anti-misogyny legislation for this purpose too.