Are the prayers performed after ablution with small white lines—presumably from soap residue—on the hands valid, knowing that water does not reach the skin because of them?

If there is a real barrier preventing water from reaching the skin, then the ablution (wudu') is invalid, and all prayers performed with this invalid ablution must be repeated. The making up (qada') of these prayers continues until one is reasonably certain that their duty has been fulfilled. However, if it is merely a case of obsessive doubts (waswasah), then the ablution is valid. It should be noted that some scholars consider the prayer of one who omits a condition or pillar out of ignorance or forgetfulness to be valid, and according to this view, the prayers are valid and do not need to be repeated.