> Without having already done the classes you did, it would be very difficult to motivate category theory and it's liable to just make students' eyes glaze over.
There's enough motivation for category theory even in basic foundations. You could start by teaching a structural set theory like ETCS as the formal counterpart of naïve set theory. Then yes, teach abstract algebra as usual but introduce category-theoretical generalizations early instead of duplicating content.
I think category theory can help to give a "roadmap" for what the basic theorems of each course will be. Personally, as a student, I always felt like my courses jumped around too much without explanation, and like I could never see what was coming next. Knowing category theory has helped me see the bigger picture. When we encounter a new category, it helps to understand what products, limits, colimits, functors, natural transformations, Yoneda Lemma, adjunctions, etc. look like for this category. Indeed, most of the theorems in a topology or algebra or measure theory course fit into this mold -- we define what a morphism is and then prove a bunch of facts about products, functors, etc..
We should teach the bulk of Lawvere theories only once. Students should get to know groups and rings as two flavors of a similar construction, and also be introduced to the mysterious fact that some objects, like fields, don't fit into the Lawvere-theory paradigm.
There's enough motivation for category theory even in basic foundations. You could start by teaching a structural set theory like ETCS as the formal counterpart of naïve set theory. Then yes, teach abstract algebra as usual but introduce category-theoretical generalizations early instead of duplicating content.