It isn't easy to change the minds of ignorant people who refuse to accept the concept that one's identity is not the same as their assigned biological sex. However, it shouldn't be difficult to make up your own mind, and that is what is really important. The truth is that one's identity on the inside is far more important than the outside, and people should be empowered to express themselves in the ways that they see fit as opposed to being forced to be something they are clearly not on the inside.
Transitioning brings our physical appearance and biological nature extremely close to our desired sex. Basically, science has revealed that all secondary sex characteristics are hormone driven; therefore, the only things that make us different from biological woman is that we can't give birth (yet) and that we manage our hormone levels medicinally. Once you are on hormones for long enough, pretty much everything in there will function the same as a female.
Nobody is required by the laws governing the universe to reflect on the inside a mirror image of the things that we do not have the power to change. Because of this fact, people for ages have expressed themselves and have made progress. Now we live in a unique and wonderful time where we are empowered to do this legitimately within society. People who don't understand will attempt to invalidate this, but never let this get to you in such a way that you allow it to invalidate yourself. Nobody would so strongly wish to be something as we must, with all that we go through, if they were not, at least mostly, women on the inside.