I had this problem too and found the specific issue. I have customized security settings on my Xbox because I only want to share and communicate with my "friends". To fix the problem, you need to loosen your security Xbox Live security settings.

1. Settings -
2. All settings -
3. Account -
4. Privacy & online safety -
5. Xbox Live privacy -
6. View details & customize -
7. Others can communicate with voice and text -
8. Select "Everybody" (Mine was set to "Friends")

The problem with this solution is that random people, anyone on Xbox Live can start texting you. I have already received random Xbox messages from people wanting to sell me stuff. Personally I do not find this solution acceptable and home that Zenimax fixes it soon.