What % can a stud be notched into for piping for the structure to still pass code?

Depends on which building code you must follow, there are many. I believe IBC does not allow notching of studs or joist at all, you must drill holes. Frequently this is require not so much for structural strength but to avoid a drywall screw or nail. Maybe one of my friends will jump in here and tell us about their local code. Which code and what year does your building department follow?

I live in Mobile, AL they use the 2006 International codes book.

Worth a double check but I am fair sure my answer is correct for IBC 2006.

Thank you.