This overwrites the touchpad settings stored in /etc/X11/xorg.conf.d/50-synaptics.conf, the default options which include two-finger middle click and three finger right click, among other options.
To avoid this in Gnome, it's needed to disable the Gnome mouse plugin in dconf to make it stop overwriting those settings with the ones selected in the GUI settings.
That was made opening dconf and uncheching the Active option in:
org -> gnome -> settings-daemon -> plugins -> mouse
Now since Cinnamon is independent from Gnome in that aspect, what is needed to be disabled is in
org -> cinnamon -> settings daemon -> plugins -> mouse
and uncheck the "Active" option.
And that's it, from now on, all the settings (such as horizontal scrolling, disabling the touchpad while typing, etc) are managed from
/etc/X11/xorg.conf.d/50-synaptics.conf
To see the actual settings being used, run synclient -l and it will print the list of options with their values. It's possible to test how they change temporarily by writing
synclient [option]=[value], for example, to set the two finger middle click:
TapButton2=2.