The two schools of thought do exist but without all the editorializing about those who hold them. Actually got to ND shortly after a clash of positions when Frank Leahy retired and "academic excellence" became the mantra of the leadership. Arrived to discover that the PE major was eliminated (not a personal issue) but discovered that in taking FR premed science I would have met all of those majors per the grad assistants as that biology class was a prerequisite for them. Have seen/heard a lot of intelligent debate between the reps of both sides over how to get a good balance for not just FB but the whole athletic program (which after FB and BB was pretty limited when I started - but that universe included NDs most successful varsity sport - fencing and the now nonexistent wrestling program.
There is another "polar" position that only got mentioned by a couple of posters below. Using revenue producing sports (still likely to be FB and BB) to fund the university. Back in the 20s ND discovered by having a good FB team playing big games on the road = big $ and profits that went and still do go into the general fund. That combined with some excellent money management of a very small endowment at the start of the Depression resulted in an expansion that included a lot of buildings. The money management "polar" folk have continued on using FB as a major source of revenue to complement fund raising and donations using the same formula for scheduling and getting its own TV network (so to speak) while keeping a national network that goes way back (I remember Joe Boland as kid).
This has played a big part in how the other polar parties have implemented decisions. In certain periods (pre Era of Ara for me as a student and pre Lou Holtz for most on the board) the $ generating game plan was disrupted by noncompetitive FB teams (not a routinely potential top 10 team) resulting in a resurgence of the t traditionalist view but just as importantly an economic decision that what needs to be done to improve FB should be done no matter despite it possibly be construed as making ND "a football factory." As noted below ND needs this money to cover the stadium complex bonds so big payday road games are going to be the norm.
Have watched over the years as these 3 perspectives have played out and think the overall pattern since the mid 50s has been to back and forth between the traditionalists with dollar folk mostly loose aligned with them and the academic excellenters who want a public image as "the Harvard of the Midwest" (a phrase from the early part of the Father Hesburgh era - not always complimentary in context BTW).
Aside: think the Kelly hire fits in as there was a collective realization that for ND to keep FB revenue up that a coach likely to wind up in the college FB Hall of Fame was the only way to go. When his era ends the cycle of "conflict" will resume as a successor is named.