Hello 
I can confirm what the student says above. When I was at Columbia all my classes were mixed with Columbia and barnard students, except for the core classes and even there some barnard students might have been in those. Activities, clubs and doems were mixed. No one cared or thought about whether one was at Barnard or Columbia. Were were all together in the band, clubs, library, courses, dining halls and anything else. I always used the Baranrd library and thohght of it as the same as one of the Columbia libraries. The meal plan at the barnard Hewitt was great and mixed with both Barnard and Columbia students. No one thought one way or the other - we were all part of Columbia University.
Many Barnard students were brilliant, and my girlfriend was a student at Barnard. There was neever a conversation I can reacall about one school or the other; and never thought about it when we would walk cross Broadway to attend the two campuses - which are really one larger campus.
PS : The Columbia admissions this year for Class of 2025 was 3.66%.
Both are outstanding colleges and I leanred wonderful things from both for which I am grateful everyday in my working career and for my personal growth.