Is it transphobic to not consider trans people to be their preferred gender while still supporting gender transition?

I fully support a trans person transitioning socially and medically because of their suffering. I view it as a medical problem with a very to successful solution. I will always use their preferred pronouns. I want the state to make transgender healthcare easily accessible. I don't want trans people being discriminated. But deep down I will always know that their chromosomes betray who they were before. I know what genitals they had before.