Is "autodidact" too obscure to use in a résumé?

I think it probably is too obscure. Put "self-learner", "self-starter", "self-taught in (some skills you want it to apply to)".

The only place where I'd expect to see such a word in a resume would be applying to an academic position where use of such words is common.

I think in general it's a bad idea to confuse the people who might be reading your resume as it could cause them to pass it over.

Every organization, every hiring manager, and every position offered is unique, so it is difficult to make a blanket rule about whether a word or phrase is suitable. After all, there is an entire industry build around résumé or c.v. writing and formatting.

Autodidact can refer to someone with skills in a subject but no formal education in a particular subject, but also to someone who is "educated" without formal schooling. I wouldn't want to be interpreted as passing myself along as a modern-day Abraham Lincoln, but I do say that I am self-taught in object-oriented programming or server administration.

You could say you are a lifelong learner. It is a pretty widely used term for adults who continue to voluntarily learn things on their own.

You could use "I am a self-learner" or "I am capable of self learning" instead.