I tried to get Dog Gone to address the issue of Nazi symapthisers in Switzerland, but she didn't think they were that important. Unfortunately, like most of Europe, Switzerland had its fascist movement, in this case the Schweizerischer Vaterländischer Verband (Swiss Patriotic Federation or SVV, French: Fédération patriotique suisse, Italian: Federazione patriottica svizzera) was a right wing organisation influential in Swiss politics before World War II.
Wikipedia discussess the SVV:
The SVV was set up in 1918 by Dr. Eugen Bircher to oppose 'international emigration', which in effect became anti-Semitism, with the group holding The Protocols of the Elders of Zion as fact, alongside a similar work Aufklärung zur Flüchtlingsfrage (Shedding Light on the Refugee Question). Bircher's position as a colonel in the Swiss Army was such that he was able to bring many high ranking officers in to the SVV, with Henri Guisan amongst those to join up. Although not specifically Nazi in its outlook it did nonetheless seek to maintain cordial relations with Nazi Germany.
Effectively open in its existence its membership was largely a closely guarded secret and as such the group became influential in driving government policy. Its influence was such that it was the only organisation with Nazi sympathies that was not closed down by the Swiss Federal Council in 1945. It was not dissolved until after it got caught up in a bribery scandal in 1948.
High-ranking officers within the Swiss Army had pro-Nazi sympathies: Such as General Henri Guisan, Colonel Arthur Fonjallaz and Colonel Eugen Bircher. General Guisan being the commander of the Swiss military.
There was a Swiss Nazi movement which was quite small, numbering only a few thousand. The party was temporarily banned in 1936 to prevent disturbances after the assassination of Landesgruppenleiter Wilhelm Gustloff of the Swiss Nazi Party by a Jewish student. Many Swiss were quite sympathetic to the racial agenda of the National Socialists. There were a variety of indigenous fascist parties in Switzerland, such as the Nationale Front and the Eidgenössische Soziale Arbeiter-Partei. Additionally, the Auslandsorganisation der NSDAP (Foreign Organization of the Nazi Party) was active in Switzerland, exploiting attitudes that were "anti-Jewish, anti-Free Mason, anti-Marxist, anti-pacifist, anti-democratic, and anti-liberal." And despite the paucity of support for the idea of joining Hitler's Reich, there were many Swiss who envisioned some kind of role for Switzerland in the Nazi New Order.
Also, Attempts by SVV to affect an Anschluss with Germany failed miserably, largely as a result of Switzerland's multicultural heritage, strong sense of national identity, and long tradition of direct democracy and civil liberties.
But, that didn't mean the Swiss were totally neutral, Donald Waters wrote a book on Swiss neutrality called "Hitler's Secret Ally". The Swiss bolstered the Nazi regime in many ways, ways that can be summarized by the following categories: border policies, opportunities for trade, and financial transactions. Behavior in all of these categories was either immoral or amoral, but Switzerland's closing of escape routes over its border is probably the most troubling. Because the Swiss feared that the appearance of "softness" with respect to its borders adjoining Nazi Germany would be an incentive for Hitler to attack (to undertake "Operation Tannenbaum"), they were highly vigilant in guarding against those attempting to cross those borders into Switzerland without the appropriate visas--in particular Jews.
Switzerland's pretend neutrality was useful to the Third Reich in that it could be used for trade and as a route for off loading its booty onto the world market. Because of the Germans' need for foreign currency and their hostility toward modern art, they were eager to dispatch impressionist and expressionist paintings to Switzerland. Perhaps the most disturbing aspect of German-Swiss art trafficking involved works looted from French Jews by the Einsatzstab Reichsleiter Rosenberg (this was a plundering unit, under the leadership of the Nazi "philosopher" Alfred Rosenberg, that stole cultural property from "enemies" of National Socialism throughout occupied Europe.
But, it was far more important that Switzerland was also Germany's banker for its stolen gold. a December 10, 1941 report from the British embassy in Washington to the U.S. Treasury Department noted that "every leading member of the governing groups in all the Axis countries have funds in Switzerland. Some have fortunes." A Nazi official responsible for foreign exchanges estimated after the war that German assets worth 15 billion Reichsmarks entered Switzerland.
So, why did Germany need to invade Switzerland when it was pretty much on the side of the Germans?