Is the list at:
    http://www.gnu.org/links/links.html#FreeGNULinuxDistributions
    the list of operating systems that meet your criteria?  It appears that 
    gNewSense includes LAME in binary format, and BLAG "recommends" it at 
    https://wiki.blagblagblag.org/Lame in much the same way OpenBSD does.

ISTR LAME is free software, but I will double-check.

    In fact, BLAG suggests other unfree programs, such as unrar 
    (https://wiki.blagblagblag.org/Unrar), even noting that the software is 
    non-free.

What is the license of Unrar?  I will try to access that page, but I
cannot access an https page except by asking someone to get it for me.
I will see if it works with plain http:.

    I don't think anyone is particularly upset that OpenBSD isn't among the 
    software you recommend, but to claim that OpenBSD includes "non-free" 
    software in its ports collection (using your definition of "free") while 
    claiming that gNewSense meets your criteria is disingenuous at best.

At best, it's an accurate statement.  At worst, the gNewSense
developers made a mistake, and will correct it.

My main basis for judging any distro is the policies it has adopted.

Everyone makes mistakes, and well-intentioned people fix their
mistakes.  So if someone finds a non-free program in gNewSense, or in
OpenBSD, in violation of the distro's policies, that's no disaster.  I
trust the developers will remove it once they find out.

On the other hand, if a distro's policies say something is allowed,
then it isn't a mistake, and I can't expect it to be fixed.  That's
what gives me stronger concern.  The presence of non-free programs
in the OpenBSD ports system is not a mistake, it's intentional.