Die-hard and Hard-core

Die-hard adjective - Tending to favor established ideas, conditions, or institutions.

Hard-core and die-hard are semantically related In some cases you can use "Hard-core" instead an adjective phrase "Die-hard".

Hard-core adjective - Firmly established over time.

Die-hard and hard-core are semantically related in dedicated topic. You can use "Die-hard" instead an adjective phrase "Hard-core", if it concerns topics such as dyed-in-the-wool.