I apologise if it's very hollow to say, Redhot, but I'm very sorry that you're faced with counteracting this attitude, with explaining nuance to people that I'd guess have only ever heard reductive narratives from cis mass media, and that you have to do all of this while they wield so much power over you in terms of providing resources. I can't imagine the stress of it and hope that taking steps like this means you're increasingly able to explore who you are so that self-understanding aids with empowering you to build a happy life.
In relation to being 'born' transgender, I'm afraid I think humanity hasn't got much of a clue about gender or how it forms. I believe I should very clearly say that I'm only a layperson with a fascination for biology so am probably very wrong about extant information and evidence. I've just tried to read all that I can and am fortunate enough to count very lovely neuroscience and genetics researchers among my social circle, some of whom are trans too. They could just be humouring my silliness or lack relevant specialist skills in the particular fields too but they've said my understanding is valid when they've been kind enough to listen to my rambling.
Ultimately, I would suggest it shouldn't matter and probably doesn't matter in this context – it may not be true of your parents but, in my view, cis people will almost always find a way to invalidate whatever is inconvenient to their understanding of gender and often seem to clad their purely emotional desire to invalidate diversity with a façade of reason after-the-fact.
As I'm sure you know, if somebody tries to come out as a child then they're told they're too young to know, that it's just a phase, that they're confusing masculinity/femininity with manhood/womanhood, that it's really that they aren't straight, that some evidence shows the incongruence often doesn't persist into puberty so that must be true of them, etc. However, if people wait to come out until later, or their identity evolve in a way where they realise being trans describes them in the present, then they're told that they should've always known, that it's too late, that socialisation makes it impossible for them to be valid, that it must be for sexual purposes, that it must just be internalised misogyny, etc. There is no magical age window when cis people will accept.
I apologise if this isn't true of your parents but I think, for me, it's commonly the case that the root consistent thing is that cis people will dismiss and invalidate due to cisnormativity and due to other factors like parents not wanting it to be true since they fear the pain for them and their child from a horrible society.
Flowing from that, if you ever feel comfortable openly discussing it and you feel the above might be the case for your parents then I'd maybe possibly suggest focusing on assuaging those root kneejerk emotions by pointing to the gains for you and the pain of not being able to be honest about yourself. Similarly, if you have access and the energy then maybe use resources like surveys on the effects of familial rejection, mental health effects of being restricted, sexuality in the community, average age when identifying or coming out, average age starting transition, diverse gender descriptors, ways the definition of trans has evolved, etc to try to dispel the idea that there is a particular rigid trans narrative and to show that the traditional narrative is, at least in my view, largely a cis creation and imposition aimed at minimising disruption by assimilating us into dominant concepts.
Of course, this is all easier said than done though and I've no doubt would be very emotionally draining and wearying. Sorry if it's too idealistic and simplistic.
Above all, best wishes and good luck. I hope you don't need the latter and I'm very sorry if the above is just a lot of self-indulgent silliness that doesn't help at all or simply patronises you by stating basic stuffs. Anxiety means I like to cover every teeny thing so nothing is missed, it's not a comment on how I see others and I apologise for you having to deal with it if it has a negative effect.
