Squatters rights is spot on.
It's also this refusal to take into account the power dynamic between men and women.
To understand that there is a massive cohort of men who are trying to stick to women.
Why would Stonewall give two shits about the ramifications of misogyny towards women? They're not a feminist organisation. The last people in their acronym they support is lesbians, women.
Them supporting a law is guaranteed to mean it benefits men at the expense of women. They may not even take into account that expense. Women just don't exist, as far as they're concerned.