What should one do who suffers from infidel-related obsessive thoughts towards someone who has committed an act of disbelief, wavering between declaring them an infidel or finding an excuse for them, along with other obsessive thoughts related to the purity of the Prophet's urine, peace and blessings be upon him?

There is no cure for obsessive thoughts more beneficial than ignoring them and not caring about them. They do not harm a person as long as he dislikes and shuns them. Allah the Almighty has not tasked Muslims with judging individual people as to whether they are disbelievers or not. It is sufficient to believe in the disbelief of those whom the Sharia has judged to be disbelievers. The default is not to declare a specific person a disbeliever until proof is established against them, and this is the matter of the Sharia judiciary. It is better to abandon these obsessive thoughts, ignore them, and busy oneself with acquiring beneficial knowledge.