Cardinal,
I think you answered your own question about whether the red book is acceptable or not. If you got the impression that the interviewer didn't like it then it seems to me that a real "green" logbook is a requirement at an interview. Unless you have some very good inside information that a particular airline is not fussy about their logbooks then I guess you should just put in the extra effort and provide a proffesional looking logbook. Personally, if I were doing the hiring and I had two candidates for one pilot position and they were both qualified, then it would come down to appearance and professionalism. A tidy logbook is just one way to get ahead in both departments! One hoop at a time!