Can you check it chat is enabled and you haven't set the chats as hidden? For example Fireteam can't be hidden but all other chat channels can.
You can see those options under: Settings -> social -> text chat
If text chat shows as Off, and attempting to change it to On causes it to automatically go back to Off again then you've got issues with either parental controls on the device blocking social features or your date of birth wasn't correctly updated.
In a recent Bungie.net update, Bungie added the ability to see the Date of Birth tied to your account via account settings with the option to update it once using KWS if its incorrect (otherwise you need to use the ticket option). You can see that via this page https://www.bungie.net/7/en/User/Account/IdentitySettings