There is essentially no pickup of noise - if at all it will be pickup of interfering signals. It depends on the type of interference: inductive coupling adds a voltage and thus is best suppressed for a high impedance signal - in the extreme case as a current loop. Capacitive coupling adds a current which has the least effect on a low impedance (can be << 50 Ohms). It might be a good idea to have one side terminated with a impedance matching the cable, to avoid resonances on the cable.
Having both sides terminated could be a problem if there is a DC current, as than changes in DC resistance (e.g. connectors) can add "noise". So if frequency allows it, I would tend to use termination at the sending side and a high input impedance. For RF signals, it is termination on both sides anyway.