This is a really good (and, in my view, important) question that is nonetheless very hard to address. There's a few elements here that make it tricky to give a straightforward answer. The US/Commonwealth covers a lot of countries (and people within them), who are of course not always going to see things the same way. Opinion polling was in its infancy, so it's hard to say with all that much certainty what any given population felt about political issues of the day. We can discuss governmental or 'official' mindsets with a bit more certainty, although even then these were hardly monolithic between or within various states.
Even within these caveats, I think it's fairly safe to say that over the course of the 1930s, fascism supplants communism as the main ideological 'enemy' of liberal democracy across the English-speaking world. One opinion poll we can point to in order to illustrate this shift comes from early 1939 - months before the Second World War broke out, and years before America entered the war - which asked US citizens who they would prefer to win in a hypothetical war between Nazi Germany and Soviet Russia. An overwhelming majority - 83%! - said Soviet Russia. Go back a decade (or forward a decade to the beginning of the Cold War) and it's hard to see how this kind of result would be repeated. The question then becomes: when and why does this shift occur. The classic answer alluded to in your question - which is basically that given by Eric Hobsbawm, who I poached the reference to the poll result above from - is that fascist, particularly Nazi, expansionism in the late 1930s became an obvious and clear threat the the European (and world) order. Hitler was at the very least willing to risk another world war, and was perhaps even seeking to start one. Once it became clear that Hitler couldn't be bought off, democratic governments and their constituents eventually realised that war against fascism was becoming inevitable.
To my mind at least, this is not a fully satisfactory answer. For one, actual Nazi expansion doesn't really get going until 1938 - well after, I would say, that public opinion towards fascism had already started to harden. We could potentially point instead to the Italian invasion of Ethiopia at the starting point of fascist expansion, but this sits awkwardly in an anti-fascist narrative - for one, beyond established anti-colonial circles, it's hard to view the international response to the Italian invasion as being all that ideologically outraged - invading African countries was not something that went beyond the pale of international politics. While it was certainly condemned by the international community, I don't think these condemnations had a particular ideological edge for the most part. This can also be seen in Italy's role in the early phases of the Second World War, only entering the war in mid-1940 (when it looked to be mostly over), and up until then had been consistently diplomatically courted by Britain and France. In fact, in purely governmental terms, it's not at all clear that the war before the Fall of France had an intrinsically ideological character in the eyes of democratic participants. Britain and France had even considered intervening in the Winter War against the Soviet Union, pointing again to a fundamental ideological ambivalence about their ongoing war against Nazi Germany, and an ingrained, habitual anti-communism. In this sense, the idea of Nazism as an existential ideological threat, not just to the European status quo but to a democratic way of life altogether, took a remarkably long time to reach the highest levels of government.
We can point to other barometers that reflect this. If we look at contemporary security concerns - policing, counter-espionage and the like - communist movements received the lion's share of official attention during the 1930s. Even somewhere like Britain, where the British Union of Fascists (BUF) actually had more members than the Communist Party of Great Britain (CPGB) for most of the 1930s, internal security agencies (MI5, Special Branch and so on) put most of their resources into surveilling and penetrating communist organisations and individuals right up to the outbreak of the Second World War. It was not until May 1940 that the BUF leader Oswald Mosley was arrested, reflecting paranoia that a 'Fifth Column' of fascist sympathisers and agents had been instrumental in enabling German success in Norway, Belgium and the Netherlands, and the example of Vidkun Quisling in Norway laid open the prospect that domestic fascists might readily collaborate with the Nazis in order to gain power. Once again, this really points to mid-1940 as being the watershed for Western governments starting to see fascism as the main ideological enemy, and even that's complicated by the Soviet Union's own abandonment of an anti-fascist foreign policy in August 1939, meaning that embracing fascism as the enemy did not immediately mean a rapprochement with communism.
But... this means that we've still got the thorny issue of why 83% of Americans, in 1939, already wanted communists to beat Nazis. Here I think we need to acknowledge a basic reality - that governments and bureaucracies are at best imperfect reflections of the people they represent. We need to remember that fascism always had opponents, particularly among the left, and the industrial working-class, many of whom were naturally a bit more inclined towards the Soviet Union and communism to begin with. What's more, the failure of the German left to oppose the rise of Nazism effectively meant that the left embarked on a great deal of soul-searching, aided by the knowledge and experience of the many German (and Italian) exiles who found refuge in the west after 1933. A key lesson was that divisions within the left - mutual suspicion between communists, socialists and liberals - had paved the way for Nazi success. This lesson was hammered home in Spain in 1936, where it looked for a while at least that a unified Spanish left was able to confront and contain a fascist-backed military uprising. In this sense, we can point to a popular anti-fascism that grew over the course of the 1930s, a movement that explicitly looked to make alliances rather than pursue sectarian goals, that looked to the Soviet Union as one of the few staunch governmental opponents of fascism rather than as an automatic enemy. At times - notably in Spain, but also France - it looked like these movements might be capable of shaping governmental policy as well, though ultimately even politicians elected on an anti-fascist platform found that they had limited options when it came to crafting an anti-fascist foreign policy. While these movements often did not succeed on their own terms - they could not prevent fascist victories in places like Spain, curtail fascist expansionism or prevent the Second World War, they did succeed I think in cementing a cultural shift away from fascism as a legitimate ideological alternative in the minds of many people.
Sources
Some of this answer boils down to: I work on aspects of the history of anti-fascism in the 1930s, and I have some thoughts about the bigger questions of how people and governments responded to the rise of fascism. Some of my earlier answers, which go into a bit more detail into what that actually looked like, and may be of interest. Beyond that, these sources are rather useful:
Michael Seidman, Transatlantic Antifascisms: From the Spanish Civil War to the end of World War II (Cambridge, 2017).
Eric Hobsbawm, The Age of Extremes (1994).
Richard Evans, The Coming of the Third Reich (2003).
Tom Buchanan, ‘Anti-fascism and Democracy in the 1930s’, European History Quarterly 32:1 (2002), pp. 39–57.
Jennifer Luff, ‘Covert and Overt Operations: Interwar Political Policing in the United States and the United Kingdom’, American Historical Review 122:3 (2017), pp. 727–757.
Nigel Copsey and Andrzej Olechnowicz (eds.), Varieties of Anti-Fascism: Britain in the Inter-War period (Basingstoke, 2010).