So, an operating system can born "free" (free as in speech, in the GNU sense)
    and then, become "non-free" just because some users decided to create a way
    to ease installations of software that "just can't be shipped with the system"?

You've formulated a very broad description, which applies to the act
of putting a non-free program in the ports system, and equally to many
other acts whose nature is different.  For instance, the program might
or might not be free; the easier way might or might not be included in
OpenBSD.  I might say the act was bad, or I might say it was good,
depending on the details not specified.

If "some users" write a way to "ease installation" of some non-free
program, and distribution D doesn't include this way in its
distribution or publicize it, then those users have done something bad
but distribution D is not responsible for what they did.

However, if distribution D includes this "easier way to install" in
its ports system, by doing so distribution D endorses it and takes on
the ethical responsibility for it.

I say "distribution D" because this is the same for any distribution,
whether it's a distribution of the BSD system, or a distribution the
GNU/Linux system, or whatever.