I'm late to this party as I was focused on buying ma hoose up in Scotland.
Yes, the UK media does seem to have fixated on the anti-trans aspect of the ruling.
I see there has also been criticism by transphobes of Scottish Equalities Minister Kaukab Stewart who said recently that a there shouldn't be a 'blanket ban' on trans women using female spaces. How dare Scotland defy the "Supreme" Court

etc.
I won't post a link because the only sources are headbangers on the far right like The Scottish Sun, Scottish Daily Express, or the paywall Times.
Whilst the world burns this is preoccupying the media writers? Even amongst Conservative members in a recent poll trans issues didn't feature in their Top Ten topics of most concern.
I never use men's loos. The idea would be abhorrent: north and south of the border I always use the Ladies. I've not had any issue and I don't detect hostility. In fact I was looking around at Glasgow airport yesterday looking for the correct loo when a lady wearing tartan came up beside me and said, 'Ours is this way, follow me.'
Unless you're J.K. Rowling I don't think most members of the public care a less. And certainly not in Scotland.
xx