Is it true by any hadith(s) or Quranic reference that purity is half of the religion?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

Abu Maalik Al-Ashʻari narrated that the Prophet, sallallaahu ʻalayhi wa sallam, said, “At-tuhoor shatr al-eemaan (purification is half of faith). 'Alhamdulillaah' fills the scales, and 'Subhaan Allaah' and 'Alhamdulillaah' fill that which is between heaven and earth. Prayer is light, and charity is proof (of one's faith), and patience is illumination, and the Quran is either an argument for you or against you. And everyone goes out in the morning to sell himself; he either sets it free or destroys it.” [Saheeh Muslim]

Al-Haafith Ibn Rajab commented on the interpretation of the word 'at-tuhoor' in the hadeeth, “The correct view adopted by most of scholars is that 'at-tuhoor' in this context means purification with water from the minor or major impurity.”

The scholars made different statements regarding the meaning of the word 'shatr' in the hadeeth. An-Nawawi wrote:

“The scholars held different views on the interpretation of the words of the Prophet: 'At-tuhoor shatr al-eemaan.' It was said that it means that the rewards of purification will be multiplied up to half the rewards of faith. It was also said that faith nullifies all past sins and that, similarly, so does ablution as it cancels out past sins, because faith is essential for the validity of the ablution; so ablution is equal in meaning to half of faith. It was also said that faith in this context refers to the prayer, as in the verse: {And never would Allaah have caused you to lose your faith...} [Quran 2:143] In this verse, Allaah referred to the prayer as faith, and the prayer will not be accepted without ablution. This is why ablution can be considered half of the prayer. This does not necessarily mean that the word shatr in the hadeeth refers to an actual half, and this is the most likely correct view. It may also mean that the parts that constitute faith are conviction in the heart and adherence to the provisions of Islam by the body parts. Hence, there are two halves to faith; the first half purifies the heart and the internal body and the second half purifies and cleanses the external body. So in this regard, the two halves make up faith.” [Sharh Saheeh Muslim]

Allaah knows best.