The differences between the cultures of Northern Ireland and England appear only in their names. In other words, Northern Ireland follows closely in England's cultural footsteps. Therefore, regardless of the implications of Brexit, Northern Ireland remains extremely similar to the rest of Britain in regards to language, recreational activities, popular food items, social behaviors, and in some regions of Northern Ireland: religion.
As a result, since Northern Ireland is too financially ill-equipped to manage their own independence, citizens of Northern Ireland will simply be happier in unification with a country that reflects their own values. The Republic of Ireland, on the other hand, actively tries to differentiate themselves from the rest of the United Kingdom— and as a result, they distance themselves from Northern Ireland. Thus, as Northern Ireland's culture remains closer to that of their British counterparts, they should remain within the United Kingdom, where they belong.