There is always some truth to the idea that if you want to really see change within a party, you have to become a member to affect that. But it doesn't mean becoming a member will affect that - it may but there are a lot of factors involved.
I don't really think that the idea that Tories inherently hate women holds much water. Many of their policies over the last decades haven't been great for women, but there are a lot of women who are Tories, lots of the best people on trans issues now are Tory women - and not just by chance, but in terms of people who seem to really understand the issues and are willing to fight for them. And while they may not claim as many women members as Labour they have not hesitated to give them real leadership and power in a way that Labour, for some reason, struggles to do.
But it's an interesting question at the moment which party might be more amenable to being changed. Tories generally seem to be more pragmatic. But the real differences between the two parties and the two positions are more ephemeral than many realise.
Traditionally leftism like that found in the UK, or my country, has a lot in common with traditional conservatism - they are much more like each other than either are like the kind of neoliberalist globalism found in the modern LP or CP. Both of those older viewpoints tend to be much more localist, more amenable to economic intervention, very much about creating social institutions which produce a functional, stable society. Both are suspicious of Big Business. Particularly in the UK there is a political tradition that really bridges both POV, the kind of approach characterised by small businesses and rural institutes, cooperative ventures, credit unions, and grass-roots organisation.
At this moment in time across much of the English-speaking world, there is a small but increasing interest in this approach among conservative parties rather than left-wing parties. You can see it in the way they have increasingly become interested in and captures the working class and rural votes, in the way they have begun to question international globalism. It's not a done deal by any means, there is still a significant group stumping for international globalism and they may win out.
But I think it would be possible right now to make a lot more headway shifting them than the modern left. Especially if instead of talking about big-state leftism there was more interest taken in small-state leftism which has in the last 50years largely fallen by the wayside - many Tory parties are pretty ripe for that kind of thinking. And they generally already think that gender ideology is dumb.