How did the democratic regimes of Britain, France and the United States avoid totalitarian takeovers while the Weimar Republic was unable to?
Of course, there is no way to know for sure why one thing happens in one society and another in another society. We can only speculate.
The most common theory is that the three countries that avoided totalitarianism were countries with relatively long histories of being democratic. The United States and Britain, in particular, had been building democratic systems and habits at least since the signing of the Magna Carta in 1215. Because they had such deep-rooted democracy, it was much harder for radical ideas to take hold and for people to turn to totalitarianism.
We must also note that the US, Britain, and France were on the winning side in WWI. They were, of course, hurt by the Depression, but that did not come on top of the hurt of losing a war and the hurt caused by the Treaty of Versailles. Therefore, people in those countries were less angry and less inclined to pursue radical ideas.
These are the most important factors that are commonly cited for why these countries avoided totalitarianism.