I think she keeps repeating the business about a possible lesbian abuser because it isn't supposed to be about lesbians being particularly at a high risk for domestic violence, that's not her underlying assumption or what she's trying to say.
As I understand people saying this, the point is that there are various individuals who could be a risk to the women in the refuge, so it's necessary to risk assess on an individual basis anyway, and it doesn't justify discrimination about a whole class of people. There s some level of truth to that, soI suspect it seems plausible in itself to quite a few people. Most people in our society have been given the message, often quite heavily, that we don't restrict groups based on the actions of individuals. Even a lot of individuals.
But there are also other reasons to have sex segregated spaces in a society, as important as the risk of violence, in some cases those are the most relevant reasons. In refuges the fact of the individuals there having fear responses to all men is very pertinent, and it makes no claim about those men being a personal danger. (And yes, presumably an abused lesbian might have a negative response to some or even many women, and that would be a hard situation that might mean a shelter wouldn't work for her.) And then there is simply the question of privacy, which the vast majority of people do have a sense of, often quite a strongly.
But here's the thing, if you have already accepted the idea that male and female aren't "real" categories, then you will see those responses as social constructs, and ones that could be removed through reeducation.
I think that while the risk issue is often the easiest to present to people, and often quite convincing, it's also going to be important to find effective ways to talk about things like privacy. We tend to shy away from it, because I think we fear it will seem prudish, or because we know there are varying cultural standards, or because it is a more complex and nuanced idea.