From the past participle of dye in the wool
- (of textiles) Dyed before being formed into cloth.
- (idiomatic, figuratively) Firmly established in a person's beliefs or habits; deeply ingrained in the nature of a person or thing.
- Smith was a dyed-in-the-wool typist and never really got used to writing on computers.
- John Major was described by his opponents as a dyed-in-the-wool Conservative.
Usage notes 
The expression "dyed in the wool" refers to a state of steadfastness, especially with respect to one's political, religious or social beliefs. The expression comes from the fact that fabric can be dyed in a number of ways. The woven fabric may be dyed after it is complete, or the threads may be dyed before they are woven. When a color is "dyed in the wool," the wool itself is dyed before being spun into threads, so the colour is least likely to fade or change. (Dyes: Webster’s Quotations, Facts and Phrases. Icon Group International. 2008, p. 344.)