I don't have twins but I took care regularly of a friends baby/toddler the same age as my firstborn when they were small.
Of course he cuddled with me, sat on my lap, I had them both in one buggy, etc so I can understand people assuming they were both mine. But even though I only heard the comments a few days a week and not EVERY day, I found them wearing.
"Are they twins" "No" "Oh, cute, are they identical?"
C'mon, I just told you they are NOT twins, how can they be identical?
"Boys or girls" "Boys" "Are they identical?"
My son was nearly hairless, blonde, blue-eyed, very light skinned, broad shouldered and very chubby.
My friends son had loads of dark curls, brown eyes, a darker skin tone and a very slender built, always on the verge of underweight.
The only thing they had in common was their height and age.
Still, I got asked every time if they were identical. Every time.
And of course the "natural" vs "Ivf" question.
Sometimes I answerd "one natural, one ivf" just to see the puzzled looks. Or if I was feeling snarky I'd ask back how they conceived their children.
Also every older person on the bus/in the supermarket/wherever who has twins in the family/neighbourhood obviously felt the need to share their story with me. It really got on my nerves but it also was quite sad often because in that generation there are a lot of dead twins. Of course I feel sorry for the surviving one, but I often did not now what to say and when they were old enough to understand it unsettled the kids to constantly hear of dead children from random people. I had loads of "Why did that womans brother die?" "Why do children die?" "Do many children die" "Will my sibling die as well?" "Will I die too before I get old?" conversations on public transport.
So OP, yes, it's probably a good idea to have some nice, some witty and some not so nice answers ready. And of course perfect the smile and nod thing.
But you definitely are NOT unreasonable to be annoyed by it!