I just went to google up membership numbers for the two parties' Oxford student branches, for comparison purposes.
Couldn't find it easily, but I think it's indicative that I thought, OK, so I'm looking for OUCA, and, er... (it's OULC by the way)
I also found an explanation of the history of the Corpus thing:
"In 2011 the Oxford Student newspaper was leaked video footage of an OCA member singing the first line of a song glorifying the Nazi Party in the Corpus Christi JCR following an OCA meeting at The Oxford Union.
The alleged incidents occurred in 2010. Current and former members of the association have strongly criticised all racism, with some members resigning, and the university launched an investigation into the society as a result of the reports.
The Dean of Corpus Christi has subsequently banned all OCA events at the college, indefinitely. "
Source = Wikipedia, so you know it's gold 
So that's why the Corpus Conservatives feel their rights are being imposed upon.
While I realise there is a Voltairesque debate to be had on the issue, I've got to confess my sympathy for them is limited.