I'd explain that there is a difference between something being a choice, and something being constant. From what you've said it sounds like they aren't familiar and/or comfortable with individuals breaking the binary boxes. I've found that even people who can accept trans* struggle with fluid, non-binary identities because they do more to disregard gender norms than what they are comfortable with. Fluid identities make people question how inherent gender is, how much of it is socially created vs. innate, why does it matter. These questions are uncomfortable, even for the initiated, but extremely so for those who aren't ready to ask themselves "Why am I a (_GENDER_)?" and "Why couldn't it change or be (_DIFFERENT GENDER_)? Personally I see gender as a blend of identity and social response, which is both innate and shaped by who we are (identity), what we do (activity), what we show (expression) and what we say (labels). Some may change or be related to choice, while others are what we feel inside and what we MUST do to be ourselves.
I identified as genderfluid before I started transitioning, with a ration of about 90%male and 10% female (AFAB). Now I tend to put myself forward as male gendered and focus on my gynandromorph sex because I can prove my body is non-binary and explain it quickly (~5min) . I still struggle with gender in private, holding onto female parts of myself because I fought so hard to be seen as male I don't want to risk losing that by doing "womanly" things. It's not a great fix, but my hope is that by teaching how natural non-binary sexes are I can get people to question their gender assumptions. Thus far, it's kind of working, but it's a long road to walk.