When you refer to someone as being “dyed-in-the-wool” what you mean is that he or she has very strong opinions about something. Opinions that are not easily changed. In other words, the person is very stubborn. His beliefs cannot be changed.
*My cousin Vindya is a dyed-in-the-wool traditionalist. She believes that a woman’s place is in the kitchen. * I understand that my grandfather was a dyed-in-the-wool conservative. * My neighbour claims to be a dyed-in-the-wool communist. But he lives in a huge house and drives a Benz.