It's fascinating that Paris Lees - an English journalist based in the UK - cites US stats to back those assertions up, when the stats on women in prison in the UK are fairly easily available.
Women in prison account for 5% of the overall prison population. 81% of that 5% are there for nonviolent crimes.
But hey, Paris is right! Women prisoners do harm women in prison! Guess which women they harm!
Themselves. They mostly harm themselves. Despite being only 5% of the prison population, women prisoners account for 28% of the prisoners who are reported for self-harming. (That's not 28% of the 5%, that's 28% of the total prison population.)
This is not really all that surprising, when you consider the women prison population as a whole: 46% have been victims of domestic violence (one agency reports 80% of the women prisoners they have contact with having suffered domestic violence). 46% of women in prison have attempted suicide at some time in their life. 53% have reported emotional, physical or sexual abuse during childhood. 31% grew up in care.
Then you add on random facts, eg that women in prison are more likely to be disciplined (for similar offences) than men in prison, and a picture really has emerged.
I don't know the stats for trans women in prison, but all the cases that I have read about in the past few years have involved violent (and incredibly violent) crimes, and often the prisoners involved haven't declared their desire to transition until they are in prison.