I’m not 100% sure how every fanbase feels and I could be wrong but I think this would be pretty close to each program’s “non negotiable” game. Some fanbases may pick each other as their top rival

:
Alabama: Auburn
Arkansas: Texas
Auburn: Alabama
Florida: Georgia
Georgia: Florida
Kentucky: Tennessee
LSU: Alabama
Mississippi State: Ole Miss
Missouri: Oklahoma
Ole Miss: Mississippi State
Oklahoma: Texas
South Carolina: Georgia
Tennessee: Alabama
Texas: Oklahoma
Texas A&M: Texas
Vanderbilt: Tennessee
So that means these team’s schedules are already set based on the above information and then you can sort the rest of the games out by most games played:
Alabama: Auburn, LSU, Tennessee
Tennessee: Alabama, Kentucky, Vanderbilt
Texas: Arkansas, Oklahoma, Texas A&M