Wouldn't the liquid take the path of least resistance to the closest tank?
No, not really and some small in line air line valves can fix any differences.
Peristalic pumps should have constant pressure.
They have constant flow rate, say 1.1 mls per minute.
Small differences in head pressure should not CHANGE this flow rate.
Personally I'd opt for different pumps for each tank.
Well, each tank is different and having a mess of dosing lines running all over is a mess. If you want to connect things from the same system, go with a central filtration system, then CO2, dosing etc, heating is all the same place.
If not, then you end up with lines running all over or you have to have the tanks all on the same rack close together, so you cannot space them nicely around the home.