Many functions of the C library are clearly marked as thread-safe or not thread-safe. For example, when I look at the manual of gmtime(3) there is a nice table that shows which of these functions are thread-safe and which aren't.
Looking at the manual page of the stat(2) function, it doesn't say one way or the other. Are functions supposed to be thread safe unless we are told otherwise?
Reading up the POSIX Safety Concept did not really clearly state that a function not marked as unsafe is safe. Maybe I missed a sentence somewhere?
The POSIX page on Thread Safety says that all functions are thread-safe except the ones listed there. stat() is not in the list, nor are any of the variants (lstat(), fstat_at(), fstat()). So it should be thread-safe.