I'm going to guess here (no way to know for sure without talking to him), that the term used was indeed a holdover from the days when Blue Discharges existed.
After Congress got rid of those discharges, they didn't stop discharging soldiers for those reasons. They just created two new discharges; "General" and "Undesirable". General was still considered honorable (and thus eligible for some veterans benefits), while "Undesirable" was not. I believe these are roughly equivalent to today's "General" and "Other Than Honorable".
"Undesirable" does seem to have been used for homosexuals (who hadn't engaged in such acts. Doing that got you a fully Dishonorable discharage instead.) until the policy was changed in the 80's. However, it was (and OTO still is) also used to discharge soldiers with mental health issues (eg: PTSD). The military is just starting to grapple with changing this policy, at least in circumstances where a psychological injury may have occurred in the line of duty.
Of course those discharges aren't limited to those causes. A person can also receive them for things like disobeying orders, adultery, fighting, drug use, or anything else your superiors don't like, but don't want to bother with convening a full courts-martial for.