Github, by default, notifies each of the team members of the activities in the repository. This is not desired when you are not active in that repository. To escape from unnecessary emails, github allows one to change "notification settings" for the repository.
By default notification is set to Watching. In all cases you pretty much want to switch to Not watching if you are not active in that repository.
When you switch to "Not Watching" then you are notified of email, only when someone pings you by using '@' or when an issue is assigned to you.
Please do not (yes do not) switch to "Ignoring". If you do that then you will not get any email notification when someone wants your attention.
You are encouraged to turn off unnecessary notifications. So do not feel that you will miss out on something that you should know if you do not keep notifications "on" for any repository. Don't have FOMO .
If you need to know something then it will be communicated to you explicitly either via email or via basecamp. You should NOT turn off notifictions from basecamp. Again keep the notifications from basecamp "ON".