I always feel that it is possible to teach abstract algebra in a simple way that follows the historical developments. An example is it is totally reasonable for me to start learning basic Galois theory after one is comfortable with linear algebra. By learning Galois theory in this way, the needs of group theory and ring (or say polynomial) theory naturally arise, and most of the materials in Dummit & Foote can be also covered.
The only obstruction I have noticed to teaching in this way is; the standard textbooks were not written in this fashion, and it is too hard to rewrite one while you know probably no one except you will use your note. However, I still believe such lecture-note/references exist, and would like to ask if you know any of such. Thank you so much.
Ian Stewart's book begins with the historical development, and classical algebra involved in studying roots of polynomials. I can't recall if you need the definitions of groups etc., but you definitely do not need much of the theory. Also the first half of the book is with complex polynomials, so no ring/field theory is really required at all.