From this link: https://linux.die.net/man/3/setlogmask logmask has per task scope not per thread scope. So we still suffer the concurrent issue if we change to group-specific logmask.
The same text appears in the more authoritative Opengroup.org web page: https://pubs.opengroup.org/onlinepubs/7908799/xsh/closelog.html
We meet that requirement in the KERNEL mode, but not in the FLAT or PROTECTED modes.
So the logmask must be in the group structure and setlogmask must become a system call at least in the FLAT and PROTECTED build. In the KERNEL build, a plain global variable as it is now is just fine. There will be one instance of the global variable in each process address space.
pthread APIs are not appropriate for use across processes (groups), so we must avoid pthread mutexes. This will not work in the KERNEL build mode because each mutex lies in a different address space. A usable mutex would have to use something like sem_open() which creates a semaphore can be used across process boundaries.
Note that setlogmask is classified as NOT thread safe: Preliminary: | MT-Unsafe race:LogMask | AS-Unsafe | AC-Safe | See POSIX Safety Concepts <https://www.gnu.org/software/libc/manual/html_node/POSIX-Safety-Concepts.html#POSIX-Safety-Concepts>. See https://www.gnu.org/software/libc/manual/html_node/setlogmask.html
So we should have no concern about thread safety. No re-entrancy protection is required. We can just remove the critical section. We do not need to use a semaphore or mutex.
Greg