All praise be to Allah.

The unnecessary strictness is not acceptable according to Islamic teachings. If a person completes his wudoo in an ordinary manner then he has obeyed to the command of Allah, may He be exalted, and has done what is required of him. You do not have to lift the part of your nail to make water reach to the skin under it. If it happens that the water does not reach that small something under the nail, then it comes under the heading of negligible matters and are pardoned. This also includes the cracks in the feet. You don’t have to make water reach inside of every crack in your feet or check them and examine them.

Just like the small amount of dirt and skin under your nail does not matter similarly same applies to the inside of the nose, even if the water does not reach where it should. This happens a great deal and to lots of people, if these things would have invalidated the wudoo then Prophet Muhammad(peace be upon him) would have explained it.

What is enjoined in the Book of Allah is to wash the face. Allah, may He be exalted, says (interpretation of the meaning):

“O you who believe! When you intend to offer As-Salat (the prayer), wash your faces…”

[al-Maa’idah 5:6].

With regard to the area under the chin, it is not included in the definition of the face, so it does not have to be washed.

Al-Kaasaani said: Because the face is what is seen when looking at a person; whatever is not seen is not part of the face.

End quote from Badaa’i‘ as-Sanaa’i‘ (1/3).

Determining what materials prevent water from reaching the skin is dependent on the nature of these materials. The scholars studied this matter, and reached the conclusion that materials are of two types:

The first type is material that has substance, i.e., it remains as a layer (on the skin), so when it is placed on the body it remains cohesive, separate from the skin, and can be removed by peeling or wiping it off.

The second type is material that has no substance, i.e., it does not form a layer, and as soon as it lands or is placed on the body, it loses its cohesiveness and it breaks down and is absorbed by the skin, and there is nothing left of it; rather only traces of it remain, such as colour and the like.

Based on that, it may be said:

If the dirt has substance in the sense that it forms a layer on the skin to the extent that it prevents water from reaching the skin, then it must be removed when doing wudoo’.

If it is simply a matter of color, or it had substance but it is very little and cannot be removed with water, then it does not make wudoo’ invalid.

And Allah knows best.