There is no doubt that the water that may get onto one’s clothes or body from the tap is taahir (pure), because the tap water is pure. 

But if the water that gets on the clothes is water with which the impurity has been washed away, then the ruling on this water is that when it separates from the impurity, if some of its characteristics have been changed by the impurity, then it is najis (impure), so if it gets on to the clothes or body, the part it has got onto must be washed. But when it separates from the impurity but has not changed, then it is taahir (pure) and it does not matter if it gets onto the body or clothes. 

This is the view of Imam Maalik (may Allah have mercy on him). See al-Mawsoo‘ah al-Fiqhiyyah, 29/99 

It should be noted with regard to this matter that the Shaytaan may try to whisper (waswaas) to the individual so as to make his go to extremes in this matter, which is contrary to Islamic teaching. It is not appropriate to have doubts about the water that is splashed when relieving oneself, unless the Muslim is definitely certain that this water carries some impurity, and that may be known from changes in the colour or smell of the water as a result of that impurity. In that case, he should wash off whatever has got onto his body or clothes. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

With regard to water, it is pure in and of itself, but if it is mixed with some impurity and that is apparent, then using it is regarded as using that impurity. What is forbidden is to use it when the impurity has become mixed with it, not because it is impure in and of itself. If there is no clear sign that the impurity has become mixed with it, this doubt about the water when the water is good and there is no change in it, comes under the heading of putting oneself through unnecessary hardship, which Allah has stated is not appropriate in our sharee‘ah, and it is a restriction from which Allah has saved yus. 

It is proven that ‘Umar ibn al-Khattaab (may Allah be pleased with him) did wudoo’ using water from a Christian vessel, even though there was a possibility that the water could have been mixed with some impurity. ‘Umar ibn al-Khattaab (may Allah be pleased with him) and a companion of his passed by a downspout, and his companion said to its owner: O owner of the downspout, is your water pure or impure? ‘Umar said: O owner of the downspout, do not tell him, because he has no need to know. 

Imam Ahmad and others stated, with regard to this issue, that if water falls on a person from a downspout and the like, and there is no sign to indicate that it is impure, then he does not have to ask about it; rather doing so is makrooh.

End quote from al-Fataawa al-Kubra, 1/225, 226 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) was asked about a person who does wudoo’ in a place where people relieve themselves and there is the possibility that his garment may become impure; does he have to wash his garment? 

He replied: 

Before I answer this question, I want to say: 

This sharee‘ah – praise be to Allah – is perfect in all aspects and is suited to sound human nature that Allah has instilled in man. It came to make things easy and in fact it came to save man from confusion caused by whispers from the Shaytaan and imaginary matters for which there is no foundation. Based on that, the basic principle is that the individual and his garments are pure, so long as there is no certainty that any impurity has got onto his body or garments. This basic principle is supported by the words of the Prophet (blessings and peace of Allah be upon him) to a man who complained to him that he imagined that he felt something – namely breaking wind – when he was praying. The Prophet (blessings and peace of Allah be upon him) said: “No one should stop (praying) unless he hears a sound or notices a smell.” So the basic principle is that things remain as they are. 

If water gets onto the clothes in which they entered the washroom in which they relieved themselves, as the questioner says, who can tell whether this dampness comes from impurity such as urine or water that has changed because of contact with faeces and the like? If we are not certain that that is the case, then the basic principle is that things are pure. Granted, he may think it most likely that it has been contaminated with something impure, but so long as we are not certain, the basic principle is that things remain pure. 

So in answer to this question, we say: if they are not certain that something impure has got onto their clothes, then the basic principle is that they remain pure and they do not have to wash their clothes; they can pray in them and there is nothing wrong with that. And Allah knows best. End quote. 

Majmoo‘ Fataawa Ibn ‘Uthaymeen, 11/question no. 23 

And Allah knows best.