The exact problem occurred to me. I'm using Goodreader to sync PDFs to my iPad via WebDAV and I got Error 403 in Textastic (no matter SSL enabled or not).
My guess is that Office 365 servers don't accept direct username/password exchange. Maybe I'm wrong. I'll try to describe my experience with Goodreader:
1. I add a connection and type in https://*-my.sharepoint.com/personal/myUsername_myInsitutionDomain/Documents, and I leave 'User', 'Password', and 'Domain' blank;
2. I tap 'Sync', and Goodreader will try to open the URL, then in the new pop-up page Office 365 will detect my institution domain and redirect to my institution login page, where I login with my username and password;
3. Goodreader shows the directories and let me choose which folder to sync, and I can choose a sub folder beneath layers;
4. Goodreader saves the cookies so I can reconnect as long as the cookies are not expired. If expired, I need to go through Step 2 again.
Hope this can help and make WebDAV on Textastic work for Office 365. Thanks!
Customer support service by UserEcho