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Wiktionary
untouchability

n. The state or condition of being untouchable.

Wikipedia
Untouchability

Untouchability is the low status of certain social groups confined to menial and despised jobs. It is usually associated with the Hindu caste system, but similar groups exist outside Hinduism, for example the Burakumin in Japan and Hutu and Twa of Rwanda. At the beginning of the twenty-first century there were over 160 million untouchables on the Indian subcontinent.

Usage examples of "untouchability".

You who are born under this sign will do well to take fullest advantage of your air of inexperience and untouchability which, with careful husbanding, should last all your life, deluding thousands of people, some of whom ought to know better.

Their untouchability and probable virginity made them even more attractive to Shasa who enjoyed the chase as much as the kill.

I am quite accustomed, thank you very much, to having a sphere of untouchability around me.