I'm sorry. Without children I would find this this difficult but could agree to disagree so long as there was a respectful attitude of live and let live/ free to campaign on both sides and we agreed never too have children.
Once children are already in the picture, I would find this incredibly hard to deal with because whether you decide to stay together or not, your children will be taught this stuff by one of the people they live and trust most in the world.
Quite apart from someone with parental responsibility enabling your child to subject themselves to elective medical interventions which are difficult or impossible to reverse (before puberty, no less!) I would be concerned about the intellectual development of my children on a very basic level of they are being required to believe conflicting things at once.
For example, I am very curious about how your partner proposes to teach them about sex and the possibility (or not) of pregnancy in a given sexual encounter or relationship if she sees literally no difference between women and transwomen.
It's not an issue that can or should be fudged, in my opinion. It's all very well saying that you should always use a condom anyway to guard against STDs but what about in a long term relationship after both partners have been tested? Presumably your children will be made aware that in a heterosexual relationship steps still need to be taken to guard against pregnancy; presumably they will be aware that this is not the case in a lesbian or gay relationship.
How will that knowledge be applied if one of them enters into a relationship with a transwoman or transman (or indeed identify as trans themselves)?
If your daughter enters into a relationship with a transwoman and there is no difference between a woman and a transwoman, you wife presumably thinks your daughter need not bother using contraception or she deals with some cognitive dissonance in advising your daughter that she needs to do so anyway?
Genuinely baffled.
I realise this is not particularly helpful but you have my sympathies for navigating some of these basic practicalities of life. Having conflicting views on parenting is hard enough without having an underlying conflict of views about the nature of reality. I suspect you may find some good answers to how to navigate this from people who have married those of a different (or no) religion.