Easy problem today, harder problem at the time due to lack of knowledge.
They used a list proportional system (the same system used today in Germany, and similar to that used across Europe). Candidates were controlled by the party, rather than self-nominated. It's a huge oligarchical system that lends itself to enormous perversions of democracy. We have self-nominated candidates in the United States, but party primary elections and every type of election used here (MNTV, SNTV, first past the post, and run-offs) are broken and create extreme distortion, polarization, and disenfranchisement by their mathematical nature.
Democracy only works when it's actually democratic. When it's not, a polarized minority can become dominant over the majority, thus dominating the public discourse and shaping the public reason, retaining and expanding power. Most systems tend to reject whichever represents the view of the voters as a whole body; STV deals with the problems of fair and equal single-winner elections (which suppress minority voices) by proportionality for solid coalitions, capturing the median voter group as well as those minority views leaning away from the median voter in proportion to the size of the groups, which are of roughly-even size, thus introducing diversity into the conversation without lopsided a priori voting power, maximizing the efficiency of the public reason.
It's extremely obvious that Trump (his government, his admin) not being able to control the media, control speech, was a really good thing. And that's true whether it's a terrible Republican or terrible Democrat, or any other terrible politician, that is in power. If you give them one big lever of speech control to start from, they'll expand that control, you can count on that.
While the Ku Klux Klan Act of 1871 didn't, you are correct, outlaw the Klan as a group, it did authorize a whole lot of measures—including authorizing federal military force and suspension of the writ of habeas corpus, and new federal civil and criminal causes of action—to combat their actions and those of similar groups, and those authorities were liberally used in suppressing them. Describing the successful strategy as “sunlight as disinfectant” rather than massive application of force is... not grounded in fact.
I don’t know if the First Amendment would have stopped the totalitarian takeover of Germany. But it certainly would have made it harder.
I wish I had that faith but I think the Holocaust stands as a pretty big counter-argument. I'm genuinely curious about your faith, do you think that something could have been done in Germany in the 30s which would have preserved free speech and prevented the Holocaust?