OK, will try it out. Manufacturer recommends at least 0.33µ on the input, 0.1µ on the output. 10µ should do in that case. It also states "no output capacitor is need for stability" and the input cap "Required if regulator is locate an appreciable distance from power supply filter". In my case there's some 20 cm of wiring in between the two.
Still hoping to get answer to my question: is it normal for bushless pumps to mess up the power supply?