We have been looking for a cause why US users can't add characters... and we found it.
Basically we are making too many requests to the server.
I have asked API support to increase our limit.
If you want, you can help by posting on the US API forums and ask them to do the same: Increase the daily request limit for OpenRaid. Then we'll all be able to add characters again properly.
For now, unfortunately it seems impossible to add characters after a certain point in time each day. This resets at midnight. US users: I recommend to add your characters in the morning until Blizzard fixes this.
Blizzard got back to me, they'll be increasing our limit soon! Thanks everyone!