This is a bit of a big and open topic that touches on a lot of different elements, however I'll front load the "smoking gun" here before digging in to the other aspects.

Specifically in the US you have an act passed by congress in 1918 which allowed for denying anarchists entry into the US, denied anarchists a path to citizenship, and allowed for the expulsion of non-citizen anarchists from the country. And those laws were indeed made use of to clamp down on the anarchist movement in the US (hundreds were deported or imprisoned). All of which substantially incentivized anyone with anarchists leanings to not use that terminology, to not call for violent overthrow of the government publicly, and to either find some other terminology and names to use or to adopt other platforms that did not involve insurrection.

Now, to echo what /u/thesupermikey has said, and to cover the situation outside of the US as well, in large part the issue here is one of a transition from vague political movement to more precisely focused and specifically named political movements, along with consolidation of seemingly disparate but connected movements. What you see through the latter half of the 19th century and into the early 20th century (in the western world) is a huge diversity of different movements that are in various ways and various intensities opposed to the entrenched widely objectionable status quo. That status quo being a very rigid class structure, incredibly deep economic inequality, massive exploitation of the working classes by the powerful and the rich, plus racism, sexism, etc.

As I said there was a diversity of moments who were working to transform that status quo through various different means. There were a great many movements who explicitly set out to diminish the power of the rich and substantially redistribute their wealth to the working classes. Today we would label those movements socialist or communist but at the time they took on many different names and many subtly different forms. Including anarchists and anarcho-communists. Many of the "anarchists" of that time could be properly labelled as communists using the terminology we use today.

Through the 1910s, '20s, '30s, and '40s you have huge upheavals in politics and geopolitics across the world, with WWII and then the Cold War taking center stage. Just as with the Russian Revolution and the aftermath rolling into the Russian Civil War you have an eventual consolidation of competing and cooperating movements. Movements that find they have a lot in common decide to unite for strength. Movements that find they have irreconcilable differences with other competing movements find that they also need to unite with movements they don't have irreconcilable differences with for strength as well.

And too the ideas circulating out in the public zeitgeist congealed into more concrete subsets instead of a vague landscape of related ideas. And part of the dynamics at play here was that the stakes had become very high. Governments had been toppled by revolution, countries had been invaded, populations had been subject to genocide and forced labor, etc. Some ideologies became less publicly palatable, such as fascism. But also, I would say, probably anarchism as well. Especially just after WWII there was a diminished desire to burn the establishment to the ground and build paradise in its ashes. People had witnessed what burning the continent of Europe to the ground looked like up close and personal and most of them decided they didn't really like it, they looked more toward a slower pace of progress that worked within the establishment.

Also through the early 20th century a lot of other things come about that transformed the political landscape. The world economy changes dramatically and transitions into the post-industrial / modernist economy we have today. One where mass production is common, where food is plentiful and cheap, where refrigeration, telephones, electricity, automobiles, radios, etc. are ubiquitous, etc. At the same time union membership increased markedly and the political power of labor came into its own.

Remember that in the US 1910 was a time before the FDIC, before Social Security, before the 8 hour day and the 5 day week. Increasing standards of living from mass production/industry combined with improvements in pay, working conditions, worker safety, and worker rights across the western world in the early 20th century substantially robbed the more violent anti-establishment movements of their driving forces.

It's been overshadowed by the World Wars today but you need to remember that folks in the early 20th century would have been shaped by the depression. Not the 1930s Great Depression but the 1890s depression. That depression also affected the entire world, and it involved many full blown bank runs, mass unemployment, etc. Compared to the 1930s working class people had less wealth, fewer job options, fewer government resources, etc. in the 1890s, so you have to imagine how hard those years were for so many. And how much that experience informed political activists who blamed the rich and industrialists for that experience as well as the all of the ongoing deprivations and exploitations of the working classes.

The perception from the experience of the 1890s depression and the aftermath was that governments (in industrialized countries) were substantially corrupt, substantially in service to a tiny population of wealthy industrialists, and completely uninterested in the general welfare of the population overall. Fast forward to, say, 1950 and things are very different. Working conditions and wages are better, standards of living are higher, some social safety net services exist (public pensions, food assistance, work assistance), banks are more regulated and there doesn't appear to be the same sort of financial volatility that existed in the 1890s or the 1930s. And there are just generally a lot more non-farm jobs available. At the same time you have the overarching geopolitical pressure of the Cold War, and the experience of the World Wars, raising the stakes substantially for would be anarchists.

So, in the US proper full blown anarchism was specifically illegal and clamped down on, while at the same time there was a change in thinking from perceiving that violent revolution was the only route to improving the lot of the public at large to perceiving that political activism working within established systems could achieve results and was worthy of continued follow through.