Nope. Formal, civil, decent conversation has unwritten rules as well. Repeatedly and intentionally calling someone by the wrong name, wrong gender, or wrong whatever is harassment and easily goes into abuse. When it comes to government forms, medical records, or school records it simply isn't the place of the agent to decide who and what someone else is. In many instances it could be contradicting legal documents already established.
We have similar laws by default here, but when it comes to trangender people those who have a problem with it start crying "poor me" and having a self thrown pity party that they can't discriminate anymore. Such as, it doesn't matter you views on interracial marriage you simply cannot refer to the wife as her maiden name in various situations because you don't believe the marriage is valid, no more than a county clerk can check the "single" box for a married homosexual couple.
Jordan Peterson really did make an arse of himself, as he himself went unpunished for his attempted martyrdom amd how the bill still has failed to lead to his predictions.