Quote from @Nathan Gesner:
1. It's a free country. If you don't like the way they do business, you are free to work with a different brokerage.
2. Did you ask her why they require it? If she can't explain the reason, I would question her skills as an agent.
3. It's a safety issue. Female agents are especially vulnerable when showing property to strangers. Many offices require a photo ID on file in case something happens (fraud, sexual assault, murder, abusive language or behavior, etc.).
1. I'm aware.
2. Yes and was quite abrupt about it, lacking any sense of client service or sensitivity to why I might object and immediately severed our working relationship, despite that I offered several other ways to meet her needs while minimizing how much I might compromise my always safeguarded ID. In hindsight she was never the right realtor for me anyway, so I'm glad and have moved on.
3. It's not a safety issue. If it were she would have asked for it before we went out together seeing empty houses in remote areas of the county I'm looking. She didn't.