Is the buddy system mandatory outside of AIT, BCT or training environment?

It's always good to have a battle with you....but outside of BCT and AIT, it's not required unless Commands require them....especially at training exercises.

It is highly recommended for safety purposes but is not a requirement. Check to see if the organization has a policy in place on this because it varies depending upon the organization.

As others have said, outside of TRADOC environments, it's not required. However, if you are new to a post or an area, if you can't get someone to come with you, make sure someone knows where you are going, and when you expect to be back. The Army has an acronym for this: GOTWA:
G: Where are you going?
O: Others going with you?
T: Time you expect to be back
W: What happens if you don't return?
A: Actions on contact (while you are away) [usually only applicable in tactical environments]