Types of Purity and Impurity in Islam
Question

I was reading a book of jurisprudence and I came across the idea of major intangible impurity. It said that this includes Shirk, disbelief and major sins… Then it mentioned minor impurity, and said that it includes invalidating Wudu and minor sins, et cetera. How sound is this categorization? Did any of the early generations say this? I hope that you can explain in detail.
Praise be to Allah.Type of purity and impurity in Islam
Purity is of two types: tangible purity and intangible purity. Impurity is also of two types: tangible impurity and intangible impurity. 
Tangible purity is the purity from ritual impurity and tangible impurity .
Tangible impurity is things that the Lawgiver has deemed to be impure and filthy. This includes that of which the impurity is major, namely dogs, and that of which the impurity is minor, such as the urine of an infant boy. It also includes that of which the impurity is moderate, such as the impurity of urine, blood and dead animals.
The discussion about purity and impurity in a real, physical sense is what the jurists focus on in their books.
Intangible purity and intangible impurity are not the focus of the jurists, hence they only mention them rarely, by way of elaboration.
Intangible purity and intangible impurity
Intangible purity is the purity of the believer, who is free of Shirk and disbelief . Intangible impurity is the impurity of disbelief, evildoing and sin.
One of the religious texts which refer to intangible purity and impurity is the verse in which Allah, may He be exalted, says (interpretation of the meaning):
{And [mention] when the angels said, “O Mary, indeed Allah has chosen you and purified you and chosen you above the women of the worlds”} [Al `Imran 3:42]
Ibn Jarir at-Tabari said: “The words {and purified you} mean: He purified your faith of the doubts and false notions that are found in the faith of other women." (Tafsir at-Tabari  5/392)
And Allah, may He be exalted, says (interpretation of the meaning):
{Take, [O, Muhammad], from their wealth a charity by which you purify them and cause them increase, and invoke [Allah’s blessings] upon them. Indeed, your invocations are reassurance for them. And Allah is Hearing and Knowing.} [At-Tawbah 9:103]
At-Tabari said: “Here Allah, may He be exalted, says to His Prophet Muhammad (blessings and peace of Allah be upon him): O Muhammad, take from the wealth of these people who have admitted their sins and repented from them charity in order to purify them from the taint of their sins, {and cause them increase} that is, develop them and elevate them above the lowly status of the hypocrites to the status of sincere people." (Tafsir at-Tabari,  11/659)
And Allah, may He be exalted, said to the wives of the Prophet (blessings and peace of Allah be upon him):
{And abide in your houses and do not display yourselves as [was] the display of the former times of ignorance. And establish prayer and give zakah and obey Allah and His Messenger. Allah intends only to remove from you the impurity [of sin], O people of the [Prophet's] household, and to purify you with [extensive] purification.} [Al-Ahzab 33:33]
What is meant here is intangible purification.
And Allah said regarding the people of Lut:
{But the answer of his people was not except that they said, “Expel the family of Lot from your city. Indeed, they are people who keep themselves pure.”} [An-Naml 27:56]
That is, they kept themselves pure from sins and abhorrent deeds.
And Allah says:
{O you who have believed, indeed the polytheists are unclean, so let them not approach al-Masjid al-Haram after this, their [final] year.} [At-Tawbah 9:28]
Ibn al-Qayyim said: “Allah, may He be glorified, describes Shirk, zina and homosexuality as impure and evil in His Book, to the exclusion of other sins, even if those sins may also be described as impure, as the Qur’an says:
{O you who have believed, indeed the polytheists are unclean} [At-Tawbah 9:28].
And He, may He be exalted, says regarding homosexuality:
{And to Lot We gave judgement and knowledge, and We saved him from the city that was committing wicked deeds. Indeed, they were a people of evil, defiantly disobedient.} [Al-Anbiya’ 21:74]
And the homosexuals said:
{“Expel the family of Lot from your city. Indeed, they are people who keep themselves pure.”} [An-Naml 27:56]
Thus in addition to their Shirk and disbelief, they affirmed that they were evil and vile people, and that Lut and his family were people who kept themselves pure of that by avoiding it.
And Allah, may He be exalted, says regarding those who commit zina:
{Wicked women are for wicked men, and wicked men are for wicked women.} [An-Nur 24:26]
Types of impurity of Shirk
The impurity of Shirk is of two types: major impurity and minor impurity.

Major impurity is the impurity of major Shirk, which Allah, may He be glorified and exalted, does not forgive.
Minor impurity is the impurity of minor Shirk, such as a little showing off and pretending in front of other people, or swearing by a created being, or fearing him or putting one’s hope in him…

The point is that impurity may sometimes be tangible and visible, and may sometimes be intangible and hidden." (Ighathat al-Lahfan min Masa’id ash-Shaytan,  1/59)
Shaykh Ibn `Uthaymin said: What is meant by purification is cleanliness and keeping oneself free of dirt. In Islamic teaching it is of two types: intangible purity and tangible purity.
Intangible purity 
As for intangible purity, it is purity of the heart, which is free from Shirk and innovations in worshipping Allah, and also free from rancour, grudges, envy, resentment and hatred, and other such attitudes when dealing with other people who do not deserve that.…
Hence Allah, may He be glorified and exalted described the polytheists as being unclean or impure, as He, may He be exalted, says:
{O you who have believed, indeed the polytheists are unclean} [At-Tawbah 9:28].
And the Prophet (blessings and peace of Allah be upon him) stated that the believer cannot be impure, as he (blessings and peace of Allah be upon him) said: “The believer does not become impure.” This is what the believer should pay great attention to in order to purify his heart of it."(Fiqh al-‘Ibadat p. 97).
Shaykh Salih al-Fawzan said: Intangible purity means being free of Shirk, free of innovations and free of sins. Allah, may He be exalted, says:
{Indeed, they are men who keep themselves.} [Al-A`raf 7:82]
In this instance, purity is intangible and refers to avoiding acts of disobedience and sin.
Shirk is also impure. Allah, may He be exalted, says:
{Indeed the polytheists are unclean.} [at-Tawbah 9:28]
This is also intangible impurity, and Tawhid (affirming the oneness of Allah) is intangible purity." (Ash-Sharh al-Mukhtasar ‘ala Zad al-Mustaqni`, 1/52)
For more, see this category: Purity
And Allah knows best.