A third "unisex" space is not at all outing.
A unisex space is liberating.
I would use it sometimes and not other times.
A unisex space is for people (almost always women) who are stuck in a queue out the door of their single sex facility and don't have reasons they cannot share a space with men, but honestly would rather wait than walk past a row of urinals in use. (This is me).
A unisex space is for parents and carers with small children of the other sex. (This was me.)
A unisex space is for parents and carers of small children of both sexes.
A unisex space is for people who don't want to use the space that matches their sex. (This includes some trans people.)
A unisex space is for anyone who doesn't feel single sex spaces matter.
A unisex space is for anyone who is happy to use either single or uni - sex spaces for changing/peeing/whatever.
A unisex space is for people who are not trans but want to actively help trans people not stand out when using the facilities which everyone is allowed to use. (Some of these people use the term trans-ally.)
Sorry, what are the downsides?