Where we are at is that…
Adam is personally comfortable with using mixed-sex toilet facilities.
Adam has concluded that women who are uncomfortable with mixed-sex toilet facilities and therefore talk about single-sex toilets are doing so because they “haven’t been paying attention”. (I think we can infer that what they haven’t been paying sufficient attention to is Adam’s higher priority list of things that Adam is uncomfortable about.)
Therefore Adam considers it legitimate for actors/activists like Alan Cummings to describe talking about toilets as part of the “culture war”.
Adam also considers that women asking politicians to explain what they mean when using words such as “women” “reasonable” or “single sex” are launching a culture war.
We don’t know what Adam’s position would be if Alan C described talking about changing rooms as a culture war. Adam personally considers changing rooms to be more of a priority so perhaps talking about changing rooms would be acceptable, provided that doing so didn’t cause politicians seeking to form the next government too much embarrassment.