yes it was Inevitable. tensions about slavery and southern state rights were bound to explode along with calls for secession And boy did they happen. It started with the south seceding. The rest of the united states didn't take the secession seriously though until the south attacked a fort and raided it for munitions and supplies. then and only then did the civil war fully explode into a reality.
When Jeffersonian Americans sought "cultural independence" they meant that they wanted the freedom and "space" to live life the way they wished, without having to conform to the norms and customs of immigrant and other groups.