(this section contributed by the late Penni Ashe Matz)
First, be clear in yourself where the discomfort is, and be sure you're not projecting onto the transgender individual. There is a widely-accepted principle in psychology, which was said best by Herrmann Hesse, in Demian: "It is impossible to hate someone. What you dislike is that part of yourself that you do not like and which you see in that person."
Try to understand that the individual's transgender status is not a choice, just like your own non-transgender status. Being gender variant may rightfully be said to be "between one's ears," just like handedness, affectional partner preferences, and similar issues. Understand that identifying as a gender that is congruent with the genitals with which one was born is itself a form of gender expression.
It's not necessary to be open and welcoming of transgender or any other characteristic of others. But it is always advisable in human relations to turn things around and see if their meaning or validity changes. To do this, ask yourself if you would be offended if: