I am a volunteer for the nt.
There's no dress code, I try to be smart and tidy but I work outside so it is fleece and a waterproof jacket at times, heels and fashion gear would both be and look ludicrous. We don't get branded clothing, that is staff only.
Yes, we have to wear a name badge on an NT lanyard - that means visitors can spot me not just for the job but also as general help point. A brightly coloured lanyard would make it more visible. The badge also shows I am allowed in the staff areas, we don't all know each other.
I am conscious that I am giving talks about someone's ancestor as a representative of his generation. And that someone could be listening.
Ive no idea either visitors are gay or not. And sexuality is the least interesting thing about a person.
Regarding disability - the place does its best but when the only access in the house is a steep stair there are limits. People do get told what is accessible before they pay.