adjective

(of an attitude, habit, or belief) firmly established and difficult or unlikely to change; ingrained.

an entrenched resistance to change

ingrained,established,well established,long-established,confirmed,fixed,set firm,firm,deep-seated,deep-rooted,rooted,deep-set,unshakeable,irremovable,indelible,ineradicable,inveterate,immutable,inexorable,dyed-in-the-wool