You're right that it's not 민자. It should be 민짜.
- 민자 (= 민간 자본) = private(non-public) funds/capital.
- 민짜 = a simple/plain item. It describes something very basic with no fashionable design or ornamentation. It is used most often for clothes.
Describing a body part like 겨드랑이(armpit) as 민짜 is not common. I think they're saying that its flat shaped or hairless, or looks very simple in some other way.