On disks formatted with APFS in MacOS 10.13 High Sierra, files can't be shared over AFP anymore [...]
This is a popular misconception - you can back up an APFS volume to a Time Machine using AFP via Netatalk. Confusion stems from ambiguous wording on https://support.apple.com/en-gb/HT208018 :
Any Time Machine share points must be shared over SMB instead of AFP. [emphasis added]
This caught out a number of people (including me). The HT208018 support article is trying to say: you can't do fileserving of files from an APFS volume to other Macs using AFP and further, you can't use a Mac APFS volume as the destination for a Time Machine backup (see https://apple.stackexchange.com/a/299720 for a detailed explanation).
Having said all the above, you can also use Time Machine with an SMB server (such as Samba) if the SMB server advertises the correct options (see below). At the time of writing (1 Oct 2017) you're in for a mildly rocky ride when trying to use Samba because you have to do a custom compile of Samba in the near-term (it will likely be next year that an appropriate pre-built Samba turns up by default in the periodic release Linux distributions).
The patches have gone in and will likely be part of the Samba 4.8 release (currently that future release is too new to have a date on https://wiki.samba.org/index.php/Samba_Release_Planning ).
The changes are now part of Samba 4.8 and above.
[Original text below]
The short of it is keep an eye on https://github.com/samba-team/samba/pull/64 and the mailing list thread related to it over on https://lists.samba.org/archive/samba-technical/2017-September/thread.html#122882 because something like it will have to go in for Time Machine to work with Samba without extra manual configuration on the Mac.
It's unclear how much Apple care about Samba these days (which started occurring when they stopped shipping it with MacOS after the Samba project switched to be GPLv3) so I'm afraid delays are to be expected. Let's see how it goes - kevinanderson1, omor1 and Ralph seem to be making progress so good luck to them!