I guess it's just human nature to get hung up on things like that...
Literal
Such-a thing [subj-が] becomes-concern-[completely-てしまう] [nominalizer-のが] human [gen-の] nature [copula-ですね]...
気になる 'to become a concern / weigh on one's mind' (different from 気にする 'to actively worry about'). 人の性 (さが) is a literary noun for 'human nature / destiny / the way of people,' weightier than 人間の性質 and with a slightly fatalistic tinge. のが nominalizes the preceding clause as the subject of 人の性です 'it's human nature.'