In a previous question, I asked about the pros and cons of teaching rings before groups in abstract algebra. Recently, it has come to my attention that there is a third approach - a unified approach - as exemplified by Matej Brešar in his Undergraduate Algebra: A Unified Approach in which he introduces the various algebraic structures in parallel. See https://www.maa.org/press/maa-reviews/undergraduate-algebra-a-unified-approach for a review by Louisa Catalano, from which I quote:
The key novelty and unique feature of the book is that, in this first part, analogous topics on different algebraic structures are considered simultaneously (for example, the section on substructures introduces subgroups, subrings, subfields, etc., subsequently; or another example, the section on normal subgroups and quotient groups is followed by the section on ideals and quotient rings).
What are the pros and cons of taking a parallel approach to algebraic structures instead of teaching them sequentially?