Is it permissible to ignore obsessive doubts during prayer and ablution—such as forgetting the number of rak'ahs or doubting whether a limb was washed—despite the fear that the prayer might not be accepted, knowing that prayer takes a long time due to these obsessive doubts?

We advise you to consult a Muslim psychiatrist. You should always choose the easier option. Do not think about sin or punishment, for if you do not act, your problem may persist. For a prayer in which you doubt the number of rak'ahs, make it four. For a limb you doubt having washed, consider that you have washed it. And so on for every matter, choose the easier and simpler option. If you do this, you will have overcome Satan who afflicted you with this obsessive-compulsive disorder.