Someone claimed that "trans men and women both are far more likely to be raped by straight men than women are likely to be raped by trans women".
To back up this provocative claim, he linked a press release from the the Williams Institute at UCLA: Transgender people over four times more likely than cisgender people to be victims of violent crime.
I decided to dig into the numbers.
In England and Wales, 60/125 "transgender" prisoners (48%) were in for sexual offences (I use scare quotes for reasons I will elaborate later). In contrast, 19% of all prisoners were in for sexual offences. So transgender prisoners were over 150% more likely to be in for sexual offences than the prison population.
I could not find rape statistics for prisoners in total, or male prisoners, only sexual offence statistics, so let us assume for simplicity that the same proportion of transgendered prisoners as prisoners who are in for sexual offences are in for rape.
Now let us look at how likely trans people are to be in prison versus the general population.
Back to the scare quotes - the BBC notes that "those 125 transgender inmates only include people who have had a prison case conference. It won't include transgender people who haven't identified themselves to the prison service or who already have a gender recognition certificate". So the true number of trans people in prison is going to be greater than these numbers show. I will assume, though, in the absence of a reason to think otherwise, that in the unmeasured trans population, the proportion in for sexual offences is similar to that in the measured trans population.
The data has improved in the latter dataset, since it now includes "those individuals known within prison to be currently living in, or presenting in, a gender different to their sex assigned at birth and who have had a local case board". However, this still excludes undeclared trans people, so the true criminality of trans people is understated by the numbers.
On 30 Apr 2021, there were 197 trans prisoners, vs 77,808 prisoners in total.
Meanwhile, the trans population is 262,000 people, vs 59.6 million for the general population.
So 0.075% of trans people are in prison (again, this understates the true number given undeclared trans inmates - they would be less likely to be undeclared in ONS statistics due to the nature of data collection). This contrasts with 0.13% of the general population. So trans people are 42% less likely to be in prison - but since they are over 150% more likely to be in for sexual offences they are still more likely to rape (assuming the chance of getting caught is the same). So we can conclude that trans people are more likely to commit rape than the general population.
Now for the next part of the question - how often trans people are raped. Unfortunately in England and Wales, "the sample size of those who identified as transgender was insufficient to present data on prevalence of sexual assault".
I am unable to find information on trans offenders in the US that's as good as that for England and Wales (which is why I used the latter above), so keeping that in mind, I looked at the same information source used by the article the person wrongly cited to support his claim, the National Crime Victimization Survey.
A report, Violent Victimization by Sexual Orientation and Gender Identity, 2017–2020, tells us that the rate of violent crime excluding simple assault for trans people was 19.0 per 1,000 persons age 16 or older. This includes threatened, attempted, and completed occurrences of rape or sexual assault, robbery, aggravated assault.
There are no statistics on rape or sexual assault for trans people in there, only by sexual orientation. If one reads the original press release the person used, it never talks about rape or sexual assault, just violent victimisation. Plus, there is nothing in there about perpetrators - for all we know it is trans people violently victimising other trans people. In any event, based on this we can draw conclusions about neither trans men and women being raped by straight men nor women being raped by trans women.
So in conclusion, the person who claimed that "trans men and women both are far more likely to be raped by straight men than women are likely to be raped by trans women" didn't even understand the source he used and was spreading fake news.
We do now know, though, that trans people are more likely to perpetrate sexual offences (and very probably rape) than the general population.
A note on methodology:
Excluding women might change the numbers a bit, since we know that women have a much lower offending rate than men (96% of prisoners in England and Wales are male).
However, I couldn't find a breakdown of sex offences committed by trans prisoners by biological sex, or indeed of the numbers of trans prisoners by biological sex, so making comparisons is hard.
We do know from other research that trans women have a similar rate of criminality to men, and trans men have a higher rate of criminality than women, so the qualitative findings probably won't change.
I did run some numbers assuming all trans prisoners were trans women and comparing them to men as a whole, and indeed the qualitative findings didn't change, though trans people ended up looking somewhat better, since men are more criminal than women, so trans women look less overrepresented in the crime statistics.