If I have a question about an open source project on GitHub, is it considered good or bad etiquette to open a new issue for that project on GitHub and post the same question on Stack Overflow (or other, appropriate SE site)?
It would depend on the question. If you're trying to get general guidance that anyone familiar with the project might be able to offer, I don't see the harm in asking in a couple of places. But please be gracious and make sure good information spreads to both places as you get it, and watch both questions / be receptive to providing more info, well, you know how it works.
If you're trying to get information that only the authors are likely to know ... GitHub (GH) is probably your best bet - but they might direct you to ask on SO instead with the express intent of answering you there.
Conversely, asking for features or reporting bugs .. definitely for GH. If you think your question is probably going to lead to a bug, then GH is probably the best place.
It just really depends. Just use your best judgement.