I'm fortunate enough to have passing privilege now, so that's not a question that ever comes up these days. Rather, I'm in control of when I disclose to other people (and it *always* comes as a surprise when I do). I'm just a short hairy dude, and there are plenty of those about so it's hardly unusual.
But it hasn't always been this easy. I transitioned on the job, and I told my colleagues that I didn't want them telling anyone else about my history. I was looking forward to working with new hires who didn't know me 'before' so that I could have some people in my life who would just treat me like a normal human being. But of course, as soon as new people were hired some of my colleagues gossiped about me behind my back and I could always tell when it had happened because the new hire would suddenly get weird around me. When confronted on it, the excuse I was given was that they didn't want the new hire to be 'confused' about me. (I became irate and pointed out that my personal safety and private medical history are much more important than someone else's 'confusion').
I prefer to be as stealth as possible because as soon as people know you're trans, they start 'othering' you and I hate being treated like a freak show. The fewer people who know about my past, the better.