POSIX_ME_HARDER is an alias for the POSIXLY_CORRECT an environment variable that can be used for some programs, particularly those written by people exasperated by some aspect of the POSIX standards.

RMS quote from an interview with Federico Biancuzzi:

To have an excuse to say that we still support the spec, if you define the environment variable, POSIX_ME_HARDER was the original way. Then a slightly prudish board member convinced me to change it to POSIXLY_CORRECT which I now think was a mistake. I should have left it as POSIX_ME_HARDER.

See Democracy Triumphs in Disk Units. (To put this message in context, there had recently been a coup that resulted in the demise of the Soviet Union.) Despite that page suggesting that df(1) uses POSIX_ME_HARDER, at least recent versions don't. So it's not a very good alias.

$ df
Filesystem           1k-blocks      Used Available Use% Mounted on
/dev/hda3             18690576   3958640  13782496  23% /
$ POSIX_ME_HARDER=yes df
Filesystem           1k-blocks      Used Available Use% Mounted on
/dev/hda3             18690576   3958640  13782496  23% /
$ POSIXLY_CORRECT=yes df
Filesystem          512-blocks      Used Available Use% Mounted on
/dev/hda3             37381152   7917280  27564992  23% /

But it's still part of the history. :)