Congenital is indeed oft used, however it means that it is a lineage trait as well (literally from con genites (Latin) meaning with father): so whilst popular in use, not strictly correct unless unless referring to a condition suffered by progenitors as well.
From the point of view of non-physical traits: perhaps inherent, or intrinsic might serve better when dealing with psychological conditions allowing a choice for the intent you wish to construe as to the capability of the individual to resist their predestined traits: if inherent, then they may well be able to resist, if intrinsic, then the trait is so fundamental as to be an integral part and unavoidable in the long run. Innate can work too, as it stems from the Latin for in/since birth.
From Freud's perspective, sexual deviances are not inherent
i.e. not part of the basic nature of the subject
From Freud's perspective, sexual deviances are not intrinsic
i.e. not part of the integral nature of the subject
From Freud's perspective, sexual deviances are not innate
i.e. not part of the birth-state of the subject
Something just occurred to me as well, the trait, described as psychological may well have a physiological cause (brain lesions, altered brain formation) and hence be able to be classified as a more properly physical trait, which could allow you to rename the trait as such.