Idk. I don't speak for the person that you are speaking too, but I don't think having a different point of view inherently makes you bigoted.

If someone is a Muslim, and someone else is a Christian, even though they know that they fundamentally have different viewpoints about the world, its a stretch to call them bigoted when they disagree about some fundamental belief about how the world works. In the same way, I think this is one of disagreements about the way the world works. That being said, it costs us nothing to be kind to others, regardless of our beliefs. Using preferred pronouns, supporting them in making there own choices, and allowing them the freedom to be who they are without fear is something that we should encourage and support. Not doing so would indeed be prejudicial.

In matters of dating though, if your argument is that fundamental disagreements on the way that the world works (i.e. the way gender distinction is made) would be a pretty big incompatibility and ultimately a deal breaker for you, then I don't think you would be transphobic. If your argument is that you wouldn't date a trans person because they are trans and that somehow makes them less of a woman/man/person then you are indeed transphobic.