You don't know anyone's medical history. You haven't given anyone a karyotype test. You'd use a new set of names for people in many circumstances and even pronouns likely in the case of an obvious intersex condition. Your decision to call Eliot Page she against his wishes is clearly ideologically driven and hateful. A petty snub more or less.
Doing it makes you a cruel person. I'm sure you don't see yourself that way, but, newsflash, humans generally want to be "good" so most cruel people think they are good and justified in their actions. They just have some toxic/anti-social ideas rooted into their sense of morality.
In this case it seems you've convinced yourself that by snubbing transgender people you're somehow protecting... truth? BiOloGiCal ReAlItY? Gendered terms predate any concept of sex chromosomes or even gametes. Jeez Ottomans worried about their concubines getting pregnant from EUNUCHS because they didn't fully realize that testes created sperm or that sperm was separate from semen. That's why they preferred dark skinned eunuchs, so they could tell if a baby was illegitimate.... Which is just to say that if you want to be "traditional" gendered terms are about surface level assessments of a person's physical appearance and social roles considered appropriate to such an appearance, not biology. If you transported Patti Harrison[1] (a very passable trans woman) back to King Arthur's court she'd be treated like a lady I assure you.
The even more fundamental thing though is respecting people's autonomy. It's a very aggressive act to call someone by labels that they dislike. Try continually getting someone's name wrong on purpose, maybe call a guy named Ted Bruce all the time, and see how your relationship with that person develops....