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.
Settings -
All settings -
Account -
Privacy & online safety -
Xbox Live privacy -
View details & customize -
Others can communicate with voice and text -
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.