Well - it seems to me there's a bit of failure of logic here, as she's changed the nature of the question. You've asked "How can someone with XY chromosomes be a woman?", which she has taken to be a statement that "trans people aren't valid". Now "woman" has usually been accepted to have quite a clear, objective meaning (someone with XX chromosomes and not XY chromosomes - and this is also implicit in your question). So, "is someone a woman?" is equivalent on your line of questioning to "does that someone have XX chromosomes?". This is perfectly logical.
"Is someone valid?", however, is much woolier. What is it to be valid? Fucked if I know. It is presumably the opposite of being invalid, but I don't know what that is either!! If she wants to have a logical argument with you, then she needs to make the case that "woman" does not in fact mean "one with XX chromosomes" and provide an alternative definition of "woman"....but that in itself must be open to debate.
Plus - what's she reporting you for exactly? You have asked a question. Politely, with no use of pejorative language. It is, I would argue, the question that stands at the very heart of this issue.....