Is there something about you that would make people suspect you would discriminate on grounds of sexuality if you didn’t wear a badge?
Once you’ve bought into that premise, the badge, at best, only shows you are a “safe person” for LGBTQ people.
How will Muslims know you are a safe person? I’m sure you aren’t an Islamophobe so I hope you wear a badge.
And Jews of course. They aren’t any less worthy than Muslims, I’m sure you agree. What do you wear for them?
Also Christians, atheists, those with hearing loss, travellers, immigrants, people with dementia, children, black people, white people, etc etc etc.
I’m sure you get the point.
Wouldn’t it be more efficient for staff to wear badges denoting who they are unsafe around, and then everyone else can relax?