Are you posting to try and get a rise out of people? Cuz that's how weird that concern is. Has your husband ever rubbed her belly or scratch her rear? Do you consider that inappropriate contact? Stop sexualizing your cat and a routine surgery
I think that where I went wrong was in saying that it was for my cat. I can see that nobody is going to understand how I feel about them and I can see that most people would say its weird.
My question still works in other contexts. Asking for a male/female masseuse, for example. Or even a male/female groomer.
We don't have to keep discussing the fact that it's my cat, because that obviously upsets people.
Okay, in most other contexts, it's still probably sexist. By virtue of being sexist, it's probably rude.
It may be more 'understandable' in those other situations (although not always more logical--after all, one is asking the gender this person presents as--not their sexual orientation, proclivities, etc. Because a male gay
masseuse vs a lesbian
masseuse for a female patient...eh, people's preferences tend to assume that everyone is 'cisgender'), but still sexist.
If the comfort of the 'patient' (customer, patient, whatever you want to call them) is affected by the gender of the 'employee' (doctor, groomer, hair dresser, etc), then there's a "reason" for it. (Not necessarily a 'good' reason, but a reason, none the less.)