How did the term fascism come about? Did it always have its current meaning/negative connotation?

There's a slight irony here in that Grand Budapest Hotel was quite explicitly written to take place in the heyday of European fascism in interwar Central Europe - it's not just the atmosphere and aesthetics, but also the clear trajectory into the post-1945 socialist era after the main events of the story. So anachronistic is absolutely not the word to use, perhaps unusually for a Wes Anderson film.

'Fascist' as a term originated in Italy after the end of the First World War, as one of several competing ultranationalist movements in the aftermath of a war in which the costs of Italy's participation could come nowhere near justifying the benefits. With a weakened central government, growing unrest in the countryside and in industrial centres, and the recent example of the 1917 Russian Revolution fresh in everyone's minds, many middle-class Italians feared that an Italian revolution was imminent. One solution - arrived at in Italy and across much of East/Central Europe - was encouraging and supporting the growth of nationalist counter-revolutionary paramilitaries, movements able to confront and contain revolutions in the absence of strong states and loyal militaries. The Fascists - led by Benito Mussolini - grew in these postwar years from a tiny organisation in northern Italy to a significant player in local and then national politics by the early 1920s as the Partito Nazionale Fascista, distinguished by their growing capacity for organised violence against real and imagined revolutionary threats. Mussolini leveraged his role as both a prominent parliamentarian and leader of a powerful paramilitary movement (against which both military and police were unwilling to act) to become Prime Minister in late 1922, which was followed by several years of tightening Fascist control as Mussolini systemically dismantled Italy's democratic institutions and space for organised opposition to the regime.

That's a very brief overview of the specific origin of the term 'Fascism' - a sadly now-inactive user, /u/klesk_vs_xaero has written in incredible detail on Italian Fascism in the past if you want to learn more. It hopefully suffices to establish that in the era of the Grand Budapest Hotel, fascism and fascists were absolutely part of contemporary discourse, an issue that would only grow more urgent with Hitler's rise to power in the early 1930s as the head of a recognisably fascist-derived movement. However, it doesn't yet get at the substance of your main question - that is, how would Europeans outside of Italy (and later Germany) have viewed fascism? Would it have been seen as an insult?

The answer there is more complex, and might conceivably change depending on the exact timing. My personal timeline for the Grand Budapest Hotel is the late 1930s (as the city the hotel is based in actually gets invaded at the end, presumably meant to echo the expansion of Nazi Germany in the late 1930s ahead of the Second World War). By this point, 'fascist' would certainly have been understood as having negative connotations by a broad swathe of people outside of Italy and Germany. By this point, not only was a clear picture emerging of what life was like under fascism in Germany in particular - the killings, the concentration camps, the social control - the disruptive effects of fascism on the European order was also being felt, and the fears of states bordering Germany becoming more acute (with the Italian invasion of Abyssinia (1935-6) and the Spanish Civil War (1936-9) serving as further evidence. If you were at all concerned about ideals like liberty, peace and democracy, then by the mid-late 1930s you would indeed see 'fascist' as a derogatory thing to call someone. Sympathisers across borders still existed - indeed, many of them would end up more or less enthusiastically collaborating with the Nazis during the Second World War - but these were generally a minority.

Even if we allow a less specific timeline though, there would always have been people for whom 'fascist' was a term of abuse. Most obviously, European socialists were not at all blind to the danger of fascism - they and their supporters had been the original victims of Italian fascism, and socialists and communists across much of Eastern/Central Europe had directly experienced paramilitary violence and/or state repression to varying degrees. In places like Germany, socialists and communists formed their own paramilitaries to protect themselves against both state and paramilitary violence in the 1920s, with the broader aim of protecting the postwar democratic order (if you were socialist) or carrying out your own Bolshevik Revolution (if you were communist). For these groups, fascists were the most consistent enemy to be faced - in more stable political contexts like Britain this was still somewhat within the bounds of normal activism (counter-protests, disrupting planned events etc), but in places like Germany these became violent struggles for control over streets and districts that regularly lead to severe injuries and deaths. Even in Italy before Mussolini's seizure of power, socialists were well aware of the existential threat fascism posed and were outspoken in attacking it.

Yet, unless I'm significantly misremembering something from the film, it's hard to argue that any of the characters were socialists, let alone communists. More useful perhaps for understanding the particular response of the Grand Budapest Hotel staff and clients is the aristocratic disdain many nascent fascist movements faced. This was particularly acute in Germany, where Hitler's Nazis were initially viewed by many German elites as an upstart, tasteless and uncultured movement, that might be tolerated or used but never welcomed as equals. Indeed, overcoming the opposition of traditional German nationalists and conservatives was the last major hurdle Hitler faced in his rise to power - Hitler was the last of many attempted solutions to enable German elites to hold onto power in the increasingly polarised Weimar system. That's certainly not to say that no aristocratic elites threw their lot in with the Nazis earlier (indeed, the complicity of Wilhelm II's son in their rise to power is an ongoing scandal in Germany at the moment), but that it was quite possible to use fascist as a derogatory term out of pure snobbishness.

However, despite some of the main characters undoubtedly being snobs, this is still at best a partial explanation of what the film depicts. Part of what we're missing is the - undoubtedly deliberate - decision to make many of the main characters explicitly or implicitly represent those whom the Nazis persecuted. Gustave is at the very least very camp, Zero is a (non-white) refugee and the murdered lawyer Kovacs is at least implied to be Jewish. The Nazis did not hide who they saw as representing societal problems to be solved - most famously in terms of racial enemies, but also in terms of anti-social behaviour that undermined the health of the German Volk from within. As with socialists, those for whom fascism represented a very personal existential threat had every reason to oppose them.

The last missing ingredient here - and this gets into opinion and film criticism as much as history - are the limitations of Grand Budapest Hotel as a film (and Wes Anderson as a filmmaker). Opposing fascism is represented here as a fundamental moral, personal choice, that decent people must (and would) make. This viewpoint harkens back all the way to the 1930s and 1940s - for those fortunate enough to escape fascist government and occupation, it was comfortable and convenient to believe that when push came to shove, they too would make a moral stand. For those that had suffered through more direct forms of fascist rule, it became vital to seal off complicity - only a few were guilty of the worst crimes or active collaboration, while the masses had been unwillingly dragged along (or indeed had actively resisted). This was not the historical reality - most of occupied Europe made the compromises needed to in order to survive, or actively embraced the temporary opportunity fascism offered to prosper or advance their own goals. Effective resistance was hard, dangerous and thankless for most of the war, and those that succeeded best did so as part of wider, collective and heavily politicised movements. Gustave is hardly representative of those who resisted, nor in the manner of his resistance - it's an idealised version based on a particular set of individualistic liberal values, that makes sense so long as the circumstances are comfortably distant for the audience. In this sense, the film is pandering somewhat in its use of 'fascist' as a derogatory term - not because no one in the period (or even those depicted) might well have had cause to hate fascists, but because of the symbolic weight this particular defiance is accorded.