There are several operations which POSIX-compliant operating systems can do atomically with filesystem objects (files and folders). Here is a list of such presumably atomic
If you consider fcntl(2) in your list of atomic operations, you can easily build a general mutex primitive. I use the flock(1) command line tool to do this in shell scripts regularly. (flock(1) is part of the util-linux-ng package.)
flock(2) is not specified by POSIX but fcntl(2) is. I think flock(1) may use fcntl(2) in some cases (e.g. NFS).
So the algorithm is something like:
You could of course do a blocking fcntl(2), but there won't be any way to know what order each process blocks and gets woken up, so whether this is appropriate depends on the application.
Note that fcntl(2) is advisory, so it won't prevent unwanted manipulation of the data file.