Hello Andrey,
we have encountered the same issue on our on-premises GitLab instance. Have you been able to resolve this somehow?
To clear this out, any member of a group can freely toggle notifications on any issue within the group, but any non-member can’t toggle them at all. We are talking about public and internal groups and issues, so anyone is able to see and read the issue and comments, but subscribing to notification is, for some reason, allowed to group members only.
This happens for external and internal users as well, also for members of different groups.
Update: I found 2 relevant (unanswered) topics