Karl Marx

No, I don't believe Karl Marx ever wore a Basque beret, but the beret became very popular under many of his followers. The poor man, not many people have found their ideas so misused as KM (Jesus of Nazareth excepted, maybe)...

Ché Guevara of course the most (mis-)used icon, in that respect; pictured here in the beautiful puppet animation Baby Marx:

And below, the old man himself, together with Friedrich Engels:

This is the original teaser for Baby Marx, an ongoing project by Pedro Reyes that explores the intersections of mass entertainment, ideology and contemporary art. The teaser was produced for the Yokohama Triennial in Japan in 2008, and was followed by a television pilot shot in Mexico City in 2009. He worked closely with Japanese master puppeteer Takumi Ota for over a year to design and build the puppets, which Reyes explains as crafted “to cast the personality of a character in the simplest form [...] a silhouette.”

No, the best I could find regarding Karl Marx with beret is this present-day look-a-like (above).