I forgot to mention to reboot after installing XQuartz. When I initially ran Inkscape, I started XQuartz first. Then I launched Inkscape, which took its sweet time, presented a barber-pole progress while OS X performed a third-party verification, and then it presented a dialog offering to Open it. I clicked on the Open button, and it then appeared. The preceding scenario only happens the first time to launch Inkscape. Subsequent launches of Inkscape will show its name on the menu bar, and then XQuartz will launch by itself in support of Inkscape, and finally Inkscape fully appears on screen. When you quit XQuartz, it takes down Inkscape — so be sure your documents are saved.
Do you successfully have XQuartz installed? Do the above steps work for you now? I ignored the link advice about changing system preference security settings to just accommodate Inkscape.
If you are getting an application not responding, then force quit Inkscape (option-command-Esc), and start XQuartz first. Then start Inkscape, with an eye to the above paragraph on how it initially behaves. The only bug is that the developers have had years to start a native OS X port of Inkscape, and have not capitallized on it.