I've cleaned my road bike rotors like this for years and they're great afterwards, These are MTB pads/rotors on the GrInbred. Must be a bit more 'baked in' shit. Also, I've no idea what the pads are - the back one looks green. Front I think is Shimano.
I wouldn't be cleaning rotors and pads with soap, that could be the residual contaminant causing your squealing. Clean with alcohol.