IANAL but it occurred to me that the issue is one of compulsion. I will attempt an explanation.
Let's say for argument's sake, Stonewall was a fascist organisation that said to GCC, you must fire Bailey because she's black and if you don't, we will cancel you.
GCC then fired Bailey for being black.
Under the "but for" clause, it cannot be argued that GCC fired Bailey because Stonewall told them to. Because firing someone for being black is inherently wrong and all the blame is on GCC. GCC could have said, but we're not allowed/we're not racist/we don't want to/we don't care if you cancel us. But also GCC agreeing that firing Bailey because she's black, is an agreement not a response to.the cancellation threat.
What Ben Cooper KC was trying to argue was that GCC wouldn't have acted as it did if Stonewall hadn't threatened them/told them what to do.
But the judges interpreted that as something that couldn't have happened because GCC are responsible for their own actions and implied in that, is that GCC are at fault because they should not have fired Bailey for being gender-critical/sex-realist.
I would argue that the trans ideology is so pernicious and the cancellation threat so real, that there was a legitimate threat by Stonewall which caused GCC to fire her.
It's as if a strongly religious organisation said to another organisation, your employee doesn't believe in our religion and you must fire her or we will excommunicate your organisation from our religion/stop you receiving benefits/services from us. This is not realistic in the UK but might be in Iran or Afghanistan.
Arguably because GCC were reliant on Stonewall for advice, it could be argued that Stonewall's threat carried more weight. Except GCC is a barristers' chambers and so it could be argued that they should be in a better position to know the law than Stonewall. Thus their dismissal of Bailey was entirely their responsibility.
I do think gender ideology is more pernicious because it's so new and so few people and organisations are objecting publicly. But that means proving that cancellation is a legitimate threat and that GCC were in thrall to Stonewall and gender ideology.
I'm sure there are flaws in this post, but it's as close as I can get to what the judgment means.