Why did Western democracies sign the Munich Agreement?

Naivety vs realpolitik

First of all, don't fall into modern trap of idolizing democracy. Remember that for example Plato consider it second worst regime, slightly better than tyranny, and actually precursor to tyranny. Also, original meaning of demos-kratos is simply rule of the people, not necessarily parliamentary democracy. For example, Hitler considered Third Reich as a from of direct democracy, where German Volk rules directly trough their Fuhrer. USSR of course considered itself democratic, much more then liberal bourgeois democracies of the West.

And even if you have parliamentary democracy, things are far from ideal. As we could see in modern times, much depends on who has more money, media support, support of big business and finally who counts the votes. And even if you have democratic government in one country, that does not mean it is obliged to defend or spread democracy in other parts of the world. For example, US and UK gladly cooperate with Saudi Arabia and other Gulf monarchies and are enemies of much more democratic Iran.

Therefore, things in international arena are decided much more by interests and realpolitik than by some imagined ideals. Let's examine country by country:

• Britain : British longstanding policy towards continent is that it should not not allow single continental power that could unite whole of Europe against it, possibly even challenging it on high seas. In that sense, they could accept Germany as dominant in Central Europe if they block USSR and spread of communism, but not much more than that. Or, in our case, they were OK with Germany getting parts of Czechoslovakia (latter whole of Czechia and Slovakia as puppet state) . But, they could not accept demise of Poland because by then Germany would become that dominant power in Europe and British could not allow this.

• France: France was afraid of German territorial ambitions on itself (Alsace-Lorraine) , and considered that it would have very though time defending against it alone. French leftist government was against caving in to the Germans, but they could do precious little alone, plus that same government was not really popular among certain parts of French society and in French army. Therefore, they finally consented to Munich.

• Poland: Poland at that time deluded itself that Germans were lesser evil than USSR, and even dreamed about alliance with them against USSR. They also had some designs on Czech territory, and could be said that they participated in partition of Czechoslovakia. Anyway, they didn't want to let Soviet troops to pass trough their territory to Czechoslovakia and essentially that doomed any effort of relief.

• Soviet Union: USSR was at that time still engaged against Germany and Italy in Spain, and all of that was before Molotov-Ribbentrop pact. At that time they were willing to go to war in Czechoslovakia but they had their beef with Poland because of lost territory in Western Ukraine and Belarus in Polish–Soviet war. Therefore, they could not intervene.

• Other players: Among other smaller players in Europe, countries like Romania and Yugoslavia were not amused with what was happening, but they mostly wanted to keep status quo and privately hoped that Germans would be satisfied. Countries like Italy, Hungary and Bulgaria wanted revanche foe what happened in WW1 and they supported Germany. US public opinion on the other hand was mostly isolationist at the time, and wanted to leave European businesses to Europeans and to avoid another bloody war.

Overall, while today Third Reich is presented as an evil incarnate in popular media, in 1930's it was not perceived as such. Germany was just another player on international scene, certainly dangerous, but not something unheard of . And, simply saying, other countries were willing to deal with them.