What is your reaction when someone says they "don't do computers?"

Nope. My mother ( ~73 ) is the only one I can think of. She has used them, haltingly, in the past. But degenerative disc disease inhibits her typing much at one sitting, cheapness/thriftiness prevents her paying for online access and a disinclination to re-learn something she was never good at keeps her where she is.

What are the reasons someone would not use computers, aside from a disability or just plain old stupidity?

As above. As noted simple age is usually the dominate factor. My father ( ~75 ) is perfectly fluent with them to the point of being a Linux advocate. But he loves technology and gadgets. My step-mother ( ~68 ) splits the difference between my father and mother - uses them, but not with great facility.

Would you be irritated if a person who did not use computers was constantly asking you to do computer related tasks for them, things that they could easily do themselves except that they “don’t do computers?”

At times, see mother above. I usually try to steer her to libraries to kind of force her to be more independent and engaged ( sorry librarians ), but I will help if pestered enough.

And what’s a good snappy comeback when someone tells you they don’t do computers?

Eh, live is too short to be that concerned about it.