Thanks, but this problem is resolved and it's not Itch.io's fault. The secret for me was that if you're using Unity 5 for WebGL, you can't use try/catch statements in your code. So now https://lexington-games.itch.io/tempest-tale is available. Due to other problems with Unity 5 WebGL (the difficulty of saving complex objects, the 20-minute build time, and the UI still not scaling quite right despite my efforts) I find the Web player useless for a game that needs a complex UI and saving. I'll make my downloadable version be the main version in the next build.
Any idea why https://lexington-games.itch.io/dragon-fate , a Twine game, doesn't show up in Firefox?