Yes I think we could agree on the majority of that but I'd look to finish your final thought/ examine that final implication: live differently from what or from whom?
Because one major issue for me with this particular belief system is the sexism inherent and implied (rarely being brought front of mind to be examined) and therefore insidious within it.
Because if we say that this man is different (or believes himself to be different) from other men or from most people because he doesn't "identify" with masculinity and is therefore is not a man, then this is a belief that men have to be masculine to be men.
Not only do I think that the implication is a load of regressive, sexist claptrap, I do actually think it is an inherently harmful and damaging message to be giving to children.
It embeds sexist ideas, while pretending that it doesn't with softly, softly, nicey language; it's confusing (because it lacks internal logic whenever questioned and requires believers to hold two conflicting ideas in their head at once, and believe both are true - (1)Men and women can be/act/do anything they want without restriction! But (2) there is a certain type of feeling that correctly matches being a man vs a woman!); and it encourages children to question whether they think there is a 'mismatch' between their bodies and personality (which is sexist and presents a framework in which there is something 'wrong' with their bodies if their personality doesn't match a set of standards associated with that body type). Again, this would be vehemently denied by activists if confronted directly but it is inherent in the ideology. We are then back round to internal contradiction and requirement to fervently believe two conflicting things at once, IngSoc style.
I think an inherently healthier simpler and correct message is that man and woman refer to the two different sexes which means the physical role you'd play in making a baby and the way your bodies develop in adulthood to do that, but that your sex has no necessary implications or links at all to your feelings, personality, likes, dislikes etc. and it is therefore impossible for there to be a 'mismatch'.
We may not be saying to our children that we believe this sexist thing this teacher believes, but if we are presenting that as a reasonable belief that they have to respect and may choose to adopt, I think that is against their best interest because it encourages them to tacitly approve sexism and tolerate it against themselves coming from other people (not to mention all the medical issues that arise of they do indeed decide to adopt it wholesale themselves).