“faced down bravado” translates to “ignored and belittled genuine concerns”
You can see in action how this is being achieved though. The person in the article is both “head of emergency operations centre training at London Ambulance Service, and joint head of its lesbian, gay, bisexual and transgender network”
People are seeking training positions then using them to push their personal agenda.
That people are ripping the signs down and defacing them is a sign of deep frustration, allied with a feeling of powerlessness. That printed signs are being put up, rather than permanent official changes being made over a suitable timeframe suggests this is being shoved through at speed and invites vandalism.
They’ve started a battle and are trying to beat people into submission, rather than discussing the topic and attempting to reach a solution which best serves the wider community.