ingrained

adj.

1. Firmly established; deep-seated: ingrained prejudice; the ingrained habits of a lifetime.
2. Worked deeply into the texture or fiber: a carpet disfigured by ingrained dirt.

adjective

1. Firmly established by long standing: confirmed, deep-rooted, deep-seated, entrenched, hard-shell, ineradicable, inveterate, irradicable, set¹, settled. See continue/stop/pause.
2. Forming an essential element, as arising from the basic structure of an individual: built-in, congenital, connatural, constitutional, elemental, inborn, inbred, indigenous, indwelling, inherent, innate, intrinsic, native, natural. See be, native/foreign, start/end.

adj

Definition: deep-rooted
Antonyms: superficial, surface

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IN BRIEF: Firmly established, deep-seated.

The ingrained idea that, because there is no king and they despise titles, the Americans are a free people is pathetically untrue.... — Margot Asquith (1864-1945), British socialite.

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The adjective has one meaning:

Meaning #1: (used especially of ideas or principles) deeply rooted; firmly fixed or held
  Synonyms: deep-rooted, deep-seated, implanted, planted

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