I personally put anything that fits trough the door in the washing machine. This includes pads and body armour amongst other things.
One tip, anything muddy, give them a cold rinse before washing (or just a could rinse if you only want to get the mud out).
I often pop all gear (pads, camelback backpacks etc) on a cold rinse after a muddy ride to get the mud out.
Not sure if it does the machine a lot of good, but ours has so far done 9 years so can’t be too bad (although it is a Miele).
Go on, pop it in the machine! Just don’t wash too hot or on a high spin speed.