The thing to remember about the story from last month is it likely an isolated incident. Additionally, I think she declined requests I would consider reasonable, such as going back through the body scanner but with the 'male' button pushed instead, to see if the anomaly in the private parts disappears. ID documents, and any gender markers on them, should be irrelevant.
As a trans woman who opted out of having genital surgery, I'm always prepared for fun and games at security. However, it's only likely to present itself as an issue if you're selected for a body scan. I've only been through one once, and the TSA agent found the situation a whole lot more awkward than I did. She followed procedure perfectly, asking me what gender I was, and whether I wanted to be patted down by a male or female agent. Don't be offended if you're ever asked this...they're supposed to do this in case you might be genderqueer or somewhere in the middle of the spectrum (or even transitioning the other way). Confidence and courtesy is the key in these situations...not least because they're often prepared for confrontation themselves in these situations.
You should consider opting out of a body scan. If you do, you can decide whether or not to disclose your private history to the patting down agent or not.