inure: To bring (a person, etc.) by use, habit, or continual exercise to a certain condition or state of mind, to the endurance of a certain condition
Emergency room personnel become inured to the sight of blood.
Scientists working in Antarctica become inured to the cold.
Teachers in schools with weak principals become inured to indignities.
enure: (legal term) to come into operation; to take place, have effect; to be available; to be applied (to the use or benefit of a person)
For example, The new tax will enure to the benefit of all the inhabitants of Madison County.
These examples from the web indicate that inure for “habituate” has become the most common spelling on both sides of the Atlantic:
WE MUST NOT BECOME INURED TO YOUTH GUN VIOLENCE (The Boston Globe)
Germans become inured to violence against foreigners (The Independent)
Are we becoming inured to civil service carelessness? (The Telegraph)
How Inured to Mass Shootings Have We Become? (The Huffington Post)
Film audiences have long become inured to elderly actors being paired off with barely post-pubescent females. (The Guardian)
In older printed works, the spellings inure and enure occur frequently with either meaning. Both the OED and Merriam-Webster offer enure as a variant spelling, but modern usage seems to favor inure for the sense of “habituate.” It may be useful to reserve the spelling enure for the legal term.
Wordnik offers examples of the uses of enure and inure.