It is absolutely still a thing. Since the current top comment (from cletus) mentions working at Google I'll relate a story from when I interviewed there. From what I understand, I made it pretty far in the process (to the "executive committee review") and that's when they asked me to explain a gap in my resume. They pressed me for a detailed breakdown of what I did during the gap and the reasons behind it, and said that they take it seriously. This was after 8 technical interviews and after I'd passed their hiring committee. I didn't get the job, although I suspect that this was not the reason. I'm sure experience varies here, and this would likely be less of an issue at a startup or other small company where a record of getting shit done is more important, but it's worth noting.
I would recommend that if you take time off for whatever reason, prepare for questions like these and be ready to provide a succinct and compelling explanation at the drop of a hat, because being blindsided isn't fun.
Jeez, good to know. As mfalcon mentioned, freelancing would be a good fallback, but you'd still have to talk about what kind of work you were doing etc.
Unfortunately, yes. Employers, and the non-technical gateways in particular, still have the mindset of "reject for anything, weeding people out means I'm doing my job!"
Make yourself look so valuable that they wouldn't dream of rejecting you for some invented reason. If front-line resume screeners are the issue, get an existing employee to submit your resume and vouch for you and get buy-in from their boss. That way HR can't reject you on a flimsy basis.
I would recommend that if you take time off for whatever reason, prepare for questions like these and be ready to provide a succinct and compelling explanation at the drop of a hat, because being blindsided isn't fun.