Let me preface my reply with a disclaimer:
My spiritual beliefs are different from those of most people. I spent a lot of time searching for answers, and now that my questions have been answered, they stand apart from mainstream religions.
In answer to your question, I say yes, and no. I believe that we were created (as a species) to be part of the Divine Plan and that we have a specific role in it. But I do not believe that each individual was specifically designed to fill a purpose. The Creator of Worlds has more important things to do than listen to the whims and whines of people.
The way that the Universe was created was such that the Creator experiences Life through us. We were designed for a variety of looks, behaviors, and biology. That provides a variety of experiences, and when you have groups of people with all their differences, you have an even wider variety. Yet, each of us still retains our own Free Will.
Within all the varieties that constitute an expression of Life, there are people with genetic, environmental, mental, emotional, and geographic differences. All of these matter, and all of us are included. Being transgender is just one facet of our being. How we look, where we grew up, where we live, how we learn or think about things, and how we feel about things are all part of what makes us -- us.
That is all part of the reason we are here. Did someone or something point at us and say, "That one will be trans." No. The question implies that there is someone or something to blame. Blame implies that there is something wrong with us. Neither is true. It is just one of many things that make us who we are.
Is there a reason for it, or some special purpose? Yes. The purpose of Life is to experience Life. All of our varieties allow us to experience Life in different ways. If everyone were exactly the same, there would be no variety, and that would affect our ability to exercise our Free Will. One of the many factors that shape how we experience life is precisely how we choose to experience it.
Being trans exposes us to experiences that others will never experience. But it also opens up opportunities to choose which experiences we want to have.
Think about that for a bit.