Dyed-in-the-wool is a phrase that refers to someone who is deeply committed to a specific set of beliefs or principles and is unlikely to change their mind. Synonyms for this phrase include staunch, unwavering, steadfast, resolute, and unyielding. These words all convey a sense of firmness and determination in one's convictions. Other synonyms for dyed-in-the-wool include dedicated, loyal, faithful, and devoted, which speak to the idea of unwavering allegiance and devotion to a particular cause or belief system. By using these synonyms, one can effectively convey the idea of someone who is deeply committed to their beliefs and unlikely to be swayed by outside influences.