Compelled pronouns are a bad idea. I suspect the vast majority of trans and non binary people navigating the world quietly as most do would be happy to be addressed by just their name. There aren't many phrases that can't be adjusted to use a name instead of a pronoun if you find using pronouns unpalatable.
I suspect though if you search the company handbook there will be something about respecting the reasonable expectation of dignity of other work colleagues.
Many companies have policies that workers are likely to disagree with albeit, I don't suspect you would be in a majority If you were to insist a personally held belief were respected and promoted even at the erosion of another colleagues dignity. I think there was a recent court case that rightly or wrongly delivered a long and detailed judgement along those lines?
That said, freedom of expression in a democratic country can not be played down. But, whilst it is very useful in cases that cause the most controversy such as Karen White, Muslim grooming gangs and sex offenders operating under the protection of the Catholic Church we do sadly live in a democracy which has an unsavory history of detestable discrimination stretching back a long time. Think Windrush, Section 28 and the export of intolerance towards trans people in India at the time of the empire for an example.
As such in my opinion it is then imperative that your perceived reluctance to respect the persons dignity or seek an agreeable alternative such as name use isn't glossed over. Alternatively we could accept on this one occasion that you made a genuine error. However, statements on a public forum such as 'I do not believe in the gender identity' may not prove helpful in unequivocally supporting that assertion.
Of course, it is your right to challenge it and put forward an argument however, if you are seeking to remove a courtesy from one minority and that is upheld, where does it stop? If it were hypothetically to result in a law change or policy change they wouldn't just remove the protection for the characteristic you don't like or agree with, they would just remove the protection full stop. As in the recent court case, a freedom granted for the lady to openly state her disagreements and beliefs with regards to trans people openly in her office, even to the discomfort of others would have also given open season to any misogynistic swine to claim a protected belief about the superiority of males when wrongly denigrating and harassing a female colleague. A bit of a case of sometimes it's worth being careful about what you wish for.
I'll state again, I believe compelled speech is wrong and the demand or expectation of a pronoun is wrong but, in this particular case I truly believe it Is non controversial enough for you to find a way around it, e.g. using just their name in an effort to both maintain their dignity and ensure your belief remains intact.
Perhaps that isn't reasonable, who knows?