Considering TERFs absolutely want to exclude trans people from domestic violence shelters, it's relevant to the broader thread discussion.
Of course it's relevant to the broader discussion. More about that in a moment.
First, it's not about the RFs, it's about the TEs. This whole discussion is about if and when and why transwomen should be excluded from some women's spaces and activities. This is purely a TE issue. RFs are a red herring.
Obviously arguments for trans exclusion in one specific case (e.g., women's sports or women's prisons) will have implications for trans access and exclusion in the general case(s).
The advantage to talking specifically about specific cases of sex segregation is that it allows us to deal directly with biological facts and correlations with those facts. We can set aside all the cultural baggage around gender identity and acceptance. We can dispense with the anti-debate strategies of vilification in place of engagement. We can look at the facts and see what we conclude.
We can even look at the facts in the context of non-factual things like axiomatic human rights. In that context we might conclude that regardless of risk, the rights we believe in mandate that we opt for trans inclusion.
But you're trying to work it backwards. Instead of addressing a specific case of sex segregation, and seeing what the conclusion tells you about trans inclusion and exclusion more generally, you keep slipping back to the predetermined principle of trans inclusion generally in a way that consistently avoids dealing with the question of sex segregation anywhere that sex segregation matters.
I think this circles us all the way back around to the title of the thread. If we look at women's sports purely in terms of sexual dimorphism and all that comes with it, we conclude that "transwomen are not women", at least not in women's sports. This has all kinds of implications for trans inclusion generally, both in terms of sex and in terms of gender.
I think this is why you keep trying to slip away from the specific case of sex segregation in prisons, with irrelevant statistics that are part of the "broader thread of discussion".
The broader thread of discussion is full of equivocation, elision, conflation, and evasion. The purpose of focusing for a bit on clear cases of sex segregation is to ditch all that baggage and have a clear conversation at least in one small corner of the larger issue. Importing equivocation, elision, conflation and evasion into this more focused part of the debate tells me a lot about the basis of your position and your confidence in defending it honestly.