Gosh!
I was fortunate enough when I had to sign on at the job centre before, I spoke to someone during the initial process, had to tell them about my transition. They had it down on their system but made my case or file or whatever, private. And the rest was normal, I was listed as male etc.
Can she not do anything against them for discrimination? Thats bad that the people she must turn to for help, have acted this way, they clearly dont understand at all.