As can be seen in the adjunct Timeline, there were many "events" in German and Swiss history that played some part (minor or major) in the establishment of Carolina. Most of the history of what we now call Germany and Switzerland is tied up in what historians call the Holy Roman Empire, which dates back to about 1254, and lasted until its dissolution in 1806.
It stands to reason that this "empire" was frequently engaged in many wars - some completely internal, but most with neighboring nation-states, which certainly came and went during this long span of time. And, the empire itself grew and contracted over time, thanks to shifts in power. The biggest external threat to the Holy Roman Empire was the Ottoman Turks in the 1500s, who ravaged much of eastern Europe after their rapid rise to power.
The biggest internal threat to the Holy Roman Empire was, of course, the Protestant Reformation that began in the mid-1500s and continued to be a factor well into the mid-1600s and even later.
In 1568, the Spanish invaded The Netherlands and thus began what historians are now calling The Eighty Years War. At once, the Holy Roman Empire struck back at the Spanish, but not with full force. Eventually, the English and the French were drawn into this conflagration, but they managed to avoid it until around 1618 - so, their portion is handily referred to as The Thirty Years War.
The French and English were finally engaged because the Holy Roman Empire was getting nowhere with the Spanish - the Spanish had assumed the leadership of the Holy Roman Empire due to convenient marriage alliances.
To make a long story short, the Treaty of Westphalia in 1648 finally brought about the independence of The Netherlands from Spain, but just as important, this treaty brought about the independence of Switzerland from the Holy Roman Empire. Switzerland was one of the "hotbeds" of the Protestant Reformation and it certainly wanted out of the Catholic Holy Roman Empire.
Germany was not so lucky. Germany as a nation-state was not even in anyone's mind back in the Middle Ages nor during the Renaissance - it did not even get that status until very recently - 1871 to be exact.
But, there were "mini-states" that arose with Germanic roots - such as Bohemia, Moravia, Silesia, and Switzerland. These and others all fell under the Holy Roman Empire, along with non-Germanic "mini-states" such as some of the major cities of present-day Italy, among others.
What is now called Germany is where the Protestant Reformation began, and it spread across Europe causing conflict after conflict, resulting in decades-long wars throughout the continent.
In the 17th century, northern Europe was a disparate collection of fiefs and kingdoms. The Palatinate was a German-speaking region along the Rhine River, roughly where the modern German state of Rhineland-Pflaz is now located.
The period following the Protestant Reformation was a time of strong religious fervor, with Protestants fighting Catholics. Thus it was for both social and economic reasons that many wars were fought for control of the Palatinate region. About half of the population was killed. Vacant lands were re-settled by a variety of Protestants: Moravians, Calvinists, Brethren, Mennonites, French Hugenots, and Lutherans from Holland and Switzerland.
The struggle for control continued; farmers caught in the middle had their families killed, crops destroyed, and buildings burned. As a further burden, their taxes were increased to unprecedented levels to pay for the wars that were ruining them. Then in 1690 a Catholic became ruler of the Palatinate - his devotion bordered on the fanatical. He persecuted all Protestants who refused to convert.
At the time, large landholders in the British colonies were seeking settlers for their sparsely populated holdings. They distributed pamphlets up and down the Rhine Valley extolling the climate and availability of land in Carolina and Pennsylvania. The devastation brought on by the war, confiscatory taxation, and fear of religious persecution, prompted the start of the Palatine emigration to the new lands in America.
Then in the winter of 1708, yet another catastrophe befell those who had not fled. An almost unprecedented cold spell across Northern Europe killed the few remaining cattle and ruined the vineyards and fruit trees that had survived the devastation of the wars. Farmers by the thousands sold what little they had and crowded their families into riverboats for the long journey down the Rhine to the Netherlands port of Rotterdam. There they camped on the outskirts of the city in crude, reed-covered shelters.
England decided it was time to take positive measures to encourage the population of its colonies in the new world. Ships bringing troops from England to the Low Countries to fight the French were instructed to transport the Palatine refugees to England on their return trip.
In England, the Palatines were placed in a series of squalid refugee camps in and about London. At first the refugees were pitied and helped, but as the summer passed and more kept arriving, Londoners turned on them. On one occasion, feeling threatened by the influx of low-cost competition, London laborers armed with scythes, axes, and hammers attacked the Palatine immigrants in the overcrowded camps.
Responding to this social unrest, as well as fearing the spread of disease and pestilence, some refugees, including all of the Catholics, were sent back to Holland to be returned to Germany. Later that year a few were settled elsewhere in England; others were sent to Ireland and Carolina.
Christopher von Graffenried led a group of Swiss/Palatines in 1710 to settle the area around New Bern, North Carolina. In all, about 100 Swiss and 600 Palatines left Europe for New Bern. Nearly all of the Swiss arrived, however, only about half of the Palatines survived the journey to New Bern. Still others were killed during the Tuscarora Indian Wars of 1712-1715.
The settlers of New Bern in Carolina at first kept very much to themselves and had very little interaction with the other groups nearby. Within twenty (20) years, the new Swiss/Germans adopted local attire and some of the English customs, but they retained their own identity well into the next century.
So - how much "influence" did these intrepid settlers have on the colony of Carolina? Hard to say that their influence was much, but to say that it was minimal would not be true. This one will have to be answered by each individual reader.