Some women prisoners might be ok with transwomen in the estate. Not everyone has to be necessarily opposed to it.
The problem is that it has the potential for causing psychological issues for some women, even if there's no violence or intimidation from the transwomen. The distress of women should never be ignored in favour of males.
I also learned from Rhona's talk that all prisoners have personal files and there are codes that are put on your file to help prison staff manage inmates.
For example, in a male prison, if you have a prisoner who is known to be a hardcore racist or part of some white supremacist gang, he will have a code in his file that is essentially a marker for 'racist'. So if there's a situation where staff are looking to house a black prisoner, they can check the files and know not to put the black prisoner in the same cell as the white supremacist guy. Makes sense in a way to avoid potential problems.
There's also a code for those who aren't happy to be housed with trans inmates.
This has the unintended effect of some female prisoners saying they are fine sharing with trans people because they don't want to get this code put on their file that effectively labels them as a 'transphobe'. Women in prison are just as susceptible as any other women in the whole kindness malarky. They want to be seen as nice and accepting and not be labelled as a transphobe by their fellow inmates or staff. So they are less likely to express their wish to not be housed with a transwoman.