NTA. Your workplace is not the place for you to divulge personal things if you don't feel like it's appropriate. Honestly it is also not your job to ever tell anyone about what her orientation is - it is her choice every time. It sounds a little weird to me that she would be upset about you trying to be respectful. Most people legitimately don't care and don't need to know. I am sure on some level she needs to be able to process that. I would suggest some therapy so she can explore why she is putting the burden of broadcasting on you, and why it's so important to her that strangers know.