Just as "normcore" is the desire to fit in and/or not stand out fashionably, "nomcore" is a way of eating that does not distinguish one's self from mainstream food.
1) John is a porn addict who wants to overcome his addiction, so he masturbates over noncore porn, usually a blank computer screen.
2) I wanted to impress my friends at a house party by seducing a hot chick, so I locked myself into a room with her and we had noncore sex while my friends listened behind the door.
In terms of musical and fashion style, the antithesis of hardcore. To be noncore one must embody everything that is not hardcore.
Noncore people never exclusivly wear torn jeans and black band t-shirts that are too small. A male example of noncore would never wear womens jeans, as opposed to current fashion trend.