I have an earlier answer about writers and coffeehouses that I believe answers your question (although IME the cliche is more about cafes and intellectual life, not cafes and social politics):
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At the risk of "since the dawn of time, mankind has"-ing it, coffeehouses/cafes in the Euro-American world have "always" been linked with intellectual life. Their initial flourishing in 17C England, especially London, was by all accounts a purposeful, genteel, civilized alternative to the sprawling brawling world of taverns and liquor.
Early coffeehouses (the first one in England was established in 1650) successfully marketed themselves as a place for the so-called "virtuosi or wits" (in the phrasing of contemporary writer and highly opinionated Anthony Wood) semi-elites to gather, read, and above all discuss intellectual topics. In the 1660s, Short's coffeehouse put together a library of academic and literary texts for its patrons to peruse. Other coffeehouses hosted academic lectures, discussion groups, and in one case even fencing lessons (/u/Georgy_K_Zhukov can talk about the connection between academia and fencing).
Coffeehouses were thus a privileged, selective alternative to raucous tavern nights, but they were also an intellectual alternative to the world of universities. They provided a semblance of independence from patronage or oversight by state and church and older regulations--that's not to say they were sources of sedition, just that attendees were not bounded by the same limitations of instructional method that university instruction tended to follow.
And along with intellectual life, of course, they gave rise to a distinct culture or subculture surrounding them, a world of gossip and fraternizing (women were generally excluded in this era). In other words, there was a social link between coffeehouses and "that kind" of intellectual orientation as an identity. This persisted into the 18th century, and a sort of division between elite and pedestrian coffeehouses/coffeehouse cultures (no, really). While a handful of them developed reputations as centers for political or political-economic discussion along lines as specific as the maritime insurance industry, more "neighborhood"-type coffeehouses offered coffee, maybe chocolate drink, newspapers, and books.
But while these peri-modern coffeehouses firmly established the link between coffee and more freewheeling intellectual life, this was still the era when writers were writing about cafes rather than in them. For that link--and more importantly, its entrenchment in the popular romantic imagination--you have to jump a Channel and a couple hundred years. Parisian cafes had developed a similar, maybe even stronger reputation as a place for offbeat intellectual discussion--the disaffected, the bohemians, the dreamers. Victor Hugo's revolutionary students in Les Miserables (1862) call themselves the "Friends of the ABC" after the coffeehouse where they meet; Puccini has his starving artist/writer characters in La boheme (1896) take over Cafe Momus for a night.
By the late 19th century, Paris was a city on the precipitous and dramatic rise. Although it had long been a cosmopolitan center of intellectual/artistic life, the "Belle Epoque" witnessed skyrocketing population and self-conscious attention to Making Paris Even Greater. This of course drew writing and thinking and painting people of various persuasions from other countries to the city, which further buttressed its reputation in that respect.
But one of the side effects of the urban planning that bequeathed us creations like the Champs-Élysées, combined with the almost-doubling of the population from 1871-1920 (most of that growth before 1900), was the worst housing situation in the Euro-American world, especially for the substantial poor and middle class population. As a result, Paris even more so than other cities developed a system of "hotels", or tenements with really lousy (metaphorically and often literally), no-amenity studio apartment type units. These are not the de facto boarding houses for single men where housekeepers would take care of "women's work" for them, or for single working women where they could be watched and 'stay respectable.' But with no or minimal kitchen equipment (the City of Lights was...not very electrified, in fact), hotel living necessitated obtaining meals from restaurants and cafes with frequency.
The pieces are in place by World War I. But it's really the interwar Lost Generation of writers and philosophers that create the "writing in cafes" romance. Ernest Hemingway's A Movable Feast, although the title does not refer to dining in cafes all over Paris, is rife with anecdotes of his times spent drinking and discussing and contemplating and Being A Writer in cafes. Simone de Beauvoir and Jean-Paul Sartre, among others (but of course I'm going to name-check Beauvoir), perpetuated the assocation of the "bohemian" intellectual/artistic lifestyle and cafes into midcentury.
Even today, cafes in Paris will advertise themselves as having hosted the literati of the Lost Generation and their successors. You can take "cafe tours" of the famous ones. So I think it's fair to say that in the long, sung, storied, and gloried history of coffee and coffeehouses and writers, the early 20th century really cemented the mythos in popular imagination.