(Ah the sinner, what a wonderful alternative to sleep and/or writing a CV)
I'm sure the CU was at one stage affiliated with the Students Association, and I'm sure it was probably the issue of exclusivity that was the motivating factor for the disaffiliation. I do know some folk who were around at the time, so I might ask around. I would be wary of rumours of CU-based campaigns against other societies. It would be a bit of a pointless effort on the CU's part to go about doing some of the things that they have been accused of doing over the years, and certainly there has been no activity against any society or person from the CU in the past few years, if ever.
On another note, the Constitution of the CU is here:
http://www.saucu.com/index.php?n=About.ConstitutionThis is probably an outdated constitution, but the majority of it still stands.
In particular section 4.1 states that all members must "conscientiously subscribe" to the statement of faith. The statement as the Bible as the "final authority in all matters of faith and conduct" could possibly cause some friction with Roman Catholics who would recognise the authority of the Pope as equal to or greater than the Bible (I'm not terribly well versed in Catholic doctrine of Papal authority - although the Catholic Catechism seems to only suggest the Pope has authority over matters of the church?). In any case, the writers of the constitution assert that the recognition of Biblical authority is a matter fundamental to the faith.
Secondly in section 6.3, committee members must sign the Doctrinal Basis of Faith as described in section 3 (a fairly basic outline of Christian beliefs, backed up by the Bible), and section 5.2.3 requires that they be in full agreement with it. In this respect, those who do not hold these beliefs are excluded from holding committee positions. The Doctrinal Basis of faith is there to protect the societies aims, as outlined in section 2, a fairly prudent and benevolent purpose. If someone ran for office within the CU who disagreed with the Doctrinal Basis and was determined to undermine these aims, it would not be the signing of the DBF that would stop them, but hopefully the voting of the members who intend to uphold these aims.
In principle it would be possible for a large number of people to join the society, vote in a non-Christian committee and disband it, but you would have to find 300 people willing to pay £3 each and give up a few hours on a Tuesday night.