Running OpenGL app with Qt 5.7 on Ubuntu 16.04: "Could not initialize GLX"

This application is built with Qt 5.7, on Ubuntu 16.04.

When running this application (either through Qt Creator or directly on the terminal), I get this error just before I create a QOpenGLWidget:

Could not initialize GLX

That's it. This problem does NOT occur when the application is built with Qt 5.5 or 5.6. With those versions, the program runs as expected.

The application doesn't crash immediately after starting, because I do some printout that's unrelated to graphics before the window is visible.

Some Googling reveals that once upon a time, Qt Creator would crash with this error message. That is NOT the case with me; Qt Creator runs as expected.

I've attached the output of qtdiag.