Your question title is very general, and your specific question is about the pervasiveness of the Oxford comma, and wanting to give up all lists because no one agrees.
I suggest that "pervasive" depends on the type of writing (book, science, academic, or news) and--rather than give up on lists--you decide on your style guide and then handle exceptions to it as they arise.
As far I know, there is no commonly accepted style guide for resumes, so I have a short answer and a long answer on how you could proceed.
Short answer: Advise your client of the style guide you follow, and ask if they have exceptions they want you to follow.
Long answer: Choose a style guide and consistently use a decision process.
This is my decision process on whether to use the oxford comma:
- What's my authority style guide? (Chicago Manual of Style, APA Publication Manual, The Associate Press Stylebook, or other)
- Does an in-house style override the authority style?
- Regardless of in-house style, could the comma (or lack of it) make the list ambiguous?
If I still can't decide, then I open "The best punctuation book, period." by June Casagrande. (I do not know June; I just love her book. Your library might carry it.)
Here's what her book states for the different types of style guides:
Book, Science, and Academic style guides
When the final item in the series of words or phrases is preceded by a coordinating junction, especially and, insert a comma before the conjunction.
They play football, basketball, and soccer.
News style guides
When the final item in the series of words or phrases is preceded by a coordinating junction, especially and, do not insert a comma before the conjunction.
They play football, basketball and soccer.
All style guides
When the final item in the series of clauses is preceded by a coordinating junction, especially and, insert a comma before the conjunction.
In the 1980s, music was loud, hair was big, and clubs were hopping along Sunset Boulevard.