When we say something is "more deep dyed," it means that it is deeply ingrained or rooted. Some synonyms for this phrase include "inborn," "inherent," "ingrained," "deep-seated," "innate," and "fundamental." These synonyms all indicate a characteristic or quality that is inherent to a person or thing, and not easily changed. The phrase "more deep dyed" is often used to describe negative traits, like prejudice or hatred, but it can also be used to describe positive qualities, like resilience or determination. Whatever the context, these synonyms help to convey the depth and permanence of the characteristic being described.