When referring to a founding year, you cannot talk of it in a possessive form. Thus, A and B, reworded, would mean "the 1833 founding of Oberlin College..." This is illogical. Instead, it should have had the form "Oberlin College was founded in
1833..." or "Oberlin College...at its founding in 1833". In the latter case, it is not "1833" but "the founding" which belonged to Oberlin College. We are left out with C, D and E.
E "deciding on the acceptance of" is plain wordy
The difference b/w C and D is more subtle but involves a crucial difference in logical understanding. C means that Oberlin College was founded for the decision
to accept both men and women and that's why it was considered a renegade institution. Alright, you can found X for some cause
but for a decision
... I don't think so
ie Centraide was founded for the protection of underprivileged children
ie Centraide was founded for the decision to protect underprivileged children -->
D is the best answer choice. Let's break it down:
Oberlin College in Ohio was a renegade institution in deciding at its founding in 1833 to accept both men and women as students.
The portion in red is a preposition phrase. Remove it and you will the clear logic. Why was Oberlin College a renegade institution? Because it decided(in deciding) to accept both men and women as students