I think it might be the following...
1)Anyone is accepted as stated before... Members OR
2)No one is accepted... Members AND
nonmembers. (The person has to be both at the same time)
The only problem with the first one is it is using disjunction rather than conjunction ( 'or' rather than 'and' ), which the original statement does not use. However, Nameless' answer 2 makes sense that you have to have two different people one being a member and one being a nonmember.
So, what do you guys think?
1)No one is accepted... Members AND nonmembers.
2)A member has to bring a nonmember