The full sentence is:
Whether born from experience or inherent physiological or cultural differences, a possibility I abhor less or discount less than my colleague Judge Cedarbaum, our gender and national origins may and will make a difference in our judging.
"Possibility" must refer only to "inherent physiological or cultural differences", because it occurs in the parenthetical phrase, and the main clause asserts that "our gender and national origins may and will make a difference in our judging."
So it follows that she is *asserting* that gender and national origins make a difference, and not just a difference in plumbing or choice of bathroom, but "in our judging." She is further asserting that this is caused *at least* by differences in life experience, but possibly by other factors.
She is not asserting that this difference is caused by inherent phsyiological or cultural differences, but she is asserting that (a) it's possible and (b) she doesn't abhor or discount the possibility.
She may be limiting the possibility of "inherent physiological" differences influencing judgement to gender, while entertaining "cultural" differences in relation to national origin. This is plausible both because the prospect of inherent physiological ethnic differences affecting judges is highly politically incorrect, and because she doubtless knows that "Latina" is a cultural and not racial descriptor.