If he says he is, he is. When you throw out the objective science, then all that's left is someone's word for it.

No, that's incorrect.

People didn't just decide whether people should be allowed to be a gender that doesn't match their biological presentation. Any more than we decided whether people should be gay or not. We observed that there were literally hundreds of thousands of people, all around the world, whose internal sense of gender did not match their biological presentation.

We're not throwing out the objective science. Quite the contrary. Gender dysphoria exists. Psychologists have been diagnosing patients that have been experiencing the phenomena associated with gender dysphoria all over the world, in nearly all countries and society. People have been observed to act in a way that demonstrates that they have gender dysphoria, independently and without coordination, across time and culture. They consistently report not just an internal sense of self that is inconsistent with their biological presentation of gender, but trauma and anguish caused by that "mismatch."

There's lots of phenomena that are like that - where science is observing people's reported symptoms, and concluding that a condition or psychological state exists because of it. Consider tinnitus. You only know someone has tinnitus because someone says they have tinnitus. But because so many people in so many different areas report experiencing tinnitus, no one doubts it exists.

So again, if someone says they're gay, we're generally okay with accepting that they're telling the truth even though we can only "take their word for it." We'll take it with a grain of salt it if they don't do and have never done anything, at all, ever that's consistent with them being gay. But if a man says he's gay, and is out there dating other men, we don't disbelieve it just because all we can do is take their word for it. And the same is true of being trans. We know that people are trans, so there's no especial reason to disbelieve someone who reports they are trans (unless, again, it's utterly inconsistent with everything they do or say). Like gay people, the question isn't whether trans people exist, but how society is going to treat them.