Nonconformity

n. lack of conformity to conventional values or beliefs

Nonconformism is in general the refusal to conform to common standards, conventions, rules, customs, traditions, norms or laws. In specific usage (usually capitalized), however, it refers to the Protestant Christians of England who refused to "conform", or follow the governance and usages of the Church of England.
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Noun
1. lack of harmony or correspondence
(hypernym) disagreement
2. a lack of conformity
(synonym) nonconformance
(antonym) conformity, conformism
(hypernym) unorthodoxy, heterodoxy, heresy
3. unorthodoxy as a consequence of not conforming to expected standards or values
(hypernym) unorthodoxy, heterodoxy
4. failure to conform
(antonym) conformity, conformation, compliance, abidance
(hypernym) failure
(hyponym) nonobservance

(n.)
Neglect or failure of conformity; especially, in England, the neglect or refusal to unite with the established church in its rites and modes of worship.
  

The nonfulfillment of a specified requirement (see also "blemish," "defect" and "imperfection").