I'd suspect that singing outgroup anthems would have a significantly stronger group-bonding effect than singing the local national anthem or something like it, by way of implicitly setting the group against the larger society. A group of Americans singing the Internationale has a lot more to bond over than the same Americans singing along to the Star-Spangled Banner at a baseball game, and I'd expect people's emotional regulation to pick up this distinction even if it isn't borne out by explicit preferences.