Here a new issue with FMP 16 that wasn't there in previous FMP 15.
Download this file and run it first on FMP 16 to see OBJ in colour and texture not working. Don't forget to upload the texture file on your server.
Right click on the Web Viewer to "Inspect it" (error code from Web Browser).
Then try FMP 15 to see how the texture works (no CORS error).
I'm using a iMAC with OSX, latest release.