Quoting Regula Ludi in Refugees from Nazi Germany and the Liberal European States, pages 94–5:

In Bern, throughout the spring and summer of 1938, different agencies were tackling the problem of how to identify Jewish refugees at the border and distinguish them from other German travellers.⁵⁸ Anxious not to disturb ‘normal relations’ with the Third Reich, Swiss diplomats were eagerly seeking a practicable solution.

In May of 1938, Rothmund was the first to propose a visa requirement for the Jews only in an internal note. While his suggestion found the approval of colleagues from other government agencies, it did not resonate well with [Fascist] authorities. Such a provision was obviously in direct contradiction to the [Fascist] goal of removing Jews from the Third Reich. In addition, it would require mechanisms for the identification of Jews that were not yet in place.

By the end of July 1938, Swiss worries materialised: the [Third Reich] officially announced the replacement of Austrian passports by German ones.⁵⁹ Some time later in August, the idea to mark the passports of ‘non‐Aryan’ German citizens emerged in a letter by Hans Frölicher, the Swiss ambassador to Berlin.

However, the documents are not clear about whether German or Swiss negotiators first came up with this suggestion. They only testify to the persisting reluctance of the [Third Reich] to agree to any solution reducing the chances of emigration for the Jews. Eventually, in August of 1938, the Swiss threatened to reintroduce a general visa requirement. As Rothmund stressed, such a step would require German applicants to ‘present proof that they were Aryan’, which implied additional administrative work for Swiss consulates.⁶⁰

In addition, the general visa requirement would probably have failed to find federal government approval because of its unpredictable economic repercussions and potential damage to the tourist industry. As a bluff to speed up negotiations, however, it was successful. In early September, the Swiss sensed a breakthrough as the [Fascists] gave up their opposition and agreed to mark the passports of Jewish nationals, but they insisted on reciprocity. This entailed that the Swiss government condone discrimination against its own Jewish citizens.

Rothmund objected to this compromise, even though he had been the first to propose discriminatory measures, and he warned that such a step would not only alienate Swiss Jews, but also expose Switzerland internationally to the accusation of becoming embroiled in [Fascist] antisemitism. As a consequence he reiterated the demand for a general visa requirement. None of these considerations eventually entered the final agreement.

The German–Swiss Protocol of 29 September 1938 included the [Third Reich’s] promise to mark the passports of its nationals belonging to the ‘Jewish race’, to be defined according to the Nuremberg Laws, with a distinctive mark and thus prevent their holders from entering Switzerland. The mark should be a clearly visible and indelible ‘J’‐stamp, as the two parties agreed. The document also included provisions that introduced discrimination against Swiss Jews. Rothmund, who was directly involved in the last rounds of negotiations, did not endorse the agreement.

The Federal Council did not heed his reservations and adopted the Protocol in a meeting of 4 October 1938. Simultaneously, it introduced the visa requirement for ‘Non‐Aryan Germans’. It thereby allowed [Fascist] racial terminology and ‘German racial legislation to penetrate Swiss administrative law’.⁶¹ The federal authorities had to deal with the international and domestic protests that followed publication of the visa requirement.

This decision, however, was the only part of the whole story to become publicly known in 1938, in contrast to Switzerland’s active rôle in the preceding negotiations that only entered public knowledge through an Allied edition of German documents in 1953.⁶² Within days, on 15 October 1938, Sweden followed the Swiss example and signed a similar agreement with the [Third Reich].

More than ever, the federal authorities were zealously dedicated to fighting ‘foreign inundation’, but by the autumn of 1938 they had dropped all pretences, leaving no doubt of whom they had in mind when talking of ‘undesirable elements’. Official discourse no longer distinguished between Jewish foreigners and refugees but used the terms ‘emigrant’ and ‘Jew’ in an interchangeable way. And all those considered ‘emigrants’ were treated as if they were undocumented or even stateless persons.

The introduction of the visa requirement for German Jews was soon followed by mandatory visa for all ‘emigrants’ on 20 January 1939, regardless of their country of origin and subsequently also for holders of Czechoslovakian passports on 15 March 1938. Eventually, not only German Jews, but all Jews and any potential refugee had to reckon with expulsion, even when they arrived from a country that had no travel restrictions between itself and Switzerland.

As a consequence, they were trapped in a dilemma: either they risked being turned away when entering without permission or they forfeited almost any chance of acceptance when revealing their true intentions by submitting a visa application.

(Emphasis added.)

It may seem odd that the Third Reich wanted to prevent Jews and legally ‘Jewish’ people from escaping to the Swiss Confederation and the Kingdom of Sweden in the 1930s, but this was likely so as to maintain good relations with the Swiss and Swedish ruling classes, which were disinterested in providing for a huge influx of refugees.