A minor correction.  The average person will never knowingly interact with a transgender person.  After all, unless they out themselves how are you going to tell?

You can't go by appearance - if in doubt, just google "Buck Angel" or "Jazz Jennings".  For that matter, in the early 1980's Caroline Cossey was not only cast as a Bond girl in "For Your Eyes Only" but she appeared in her own Playboy pictorial - nobody knew until a few years later when one of the the UK tabloids outed her.

It's quite probable that you've interacted with a transgendered individual without ever being aware of it.