Its a Louisiana board and the majority of posters back here are LSU fans in one fashion or another. "Most hated" for some is just another way of saying "biggest rival" as fans tend to not like their rivals the most.
If you had done this poll forty years ago Ole Miss would have won with a scattering of votes going to Alabama. The Ole Miss/LSU rivalry has died out for the most part (the only really big game between the teams being the last one in Oxford with Eli which i really enjoyed going to).
LSU has no natural rival now in the sense that Aalabama and Auburn are rivals and Ohio State and Michigan are rivals. Recently LSU and Auburn have developed a rilvary as they have fought it out for the west, but it will probably never replace the Alabama/Auburn rivlary for Auburn folks(unless over a period of many, many years Alabama got really bad).
Over the past twenty years or so LSU's main rivals have been Alabama, Auburn and Florida, thats why they got the most votes. LSU got a number of votes in this poll basically because most folks on the college board who are not LSU fans resent LSU postings on the super forum.
LSU doesnt play Tennessee enough for them to be a main rival. Florida is the one East team LSU plays every year.