The events in Thuringia have shaken German politics. Ms. Merkel called the outcome “unforgivable.” Lars Klingbeil, the secretary general of the Social Democrats, spoke of a “low point in Germany’s postwar history.” Even the conservative tabloid Bild called the result a “disgrace.” After a wave of public fury — including protests across the country — Mr. Kemmerich announced on Thursday that he would resign in order to allow new elections. (It’s far from clear that a new election wouldn’t produce even stronger results for the AfD, however.)

But what led to these shameful machinations goes far deeper: the increasing normalization of the radical right in German politics. Even if Germany’s conservatives and liberals have not previously entered into formal agreements with the far right at the federal level, and are unlikely to let the AfD into a future government, they have nonetheless helped it gain power and far too often set the agenda. That dynamic won’t disappear soon.

This was not the first time that centrists have collaborated with the AfD. There have been at least 18 cases in which Ms. Merkel’s party has cooperated with the AfD on a local level, it was reported last fall. In the state parliaments of Berlin and Brandenburg, for example, the two parties have voted together on legislation. Leading Christian Democrats from several states have declared their willingness to work with the far-right party. In Saxony-Anhalt, the two parties teamed up in 2017 on an “inquiry on left extremism.” And in the same state, two Christian Democratic members of Parliament wrote a position paper last year in which they considered a coalition with the AfD. “We must reconcile the social with the national,” they stated, echoing neo-Nazi rhetoric.

The AfD has grown consistently since its founding in 2013 and is now present in the parliaments of every one of Germany’s 16 states. The parties of the center, meanwhile, have all shifted rightward. Both the Free Democrats, under their leader Christian Lindner, and the Christian Democrats have moved their policy platforms in an anti-immigrant direction. Neither Ms. Merkel nor the party’s new leader, Annegret Kramp-Karrenbauer, have created clear boundaries between their party and the far right. But many voters, especially in the east of Germany, would rather buy the original product than its copies.

How did it come to this? One major factor is the obsession of many German centrists with the so-called horseshoe theory of politics, where the far left and the far right are equivalent.