Very few tools are more useful in propaganda than simple coincidence.
The mere presence of some person at some crucial place and time, can be spun into a conspiracy theory.
Or, similarly, two events happening on the same date in different years can be exploited to obscure or compare otherwise unrelated phenomena. Two notable examples are the dates September 11 and November 11. There is no evidence that the September 11, 1973 Chilean coup had any direct relationship other than being an aspect of interventionist U.S. foreign policy, to the September 11, 2001 attacks on the US. However, this coincidence has been heavily exploited by those seeking to draw attention to - US foreign policy.
Prior to 1918, November 11 had been an anarchist holiday, playing a role similar to May 1 for the communist - it commemorated the hanging of seven anarchists in Chicago in the aftermath of a riot in the 1880s. Although there is no direct evidence that the date of the Armistice that ended World War I was chosen deliberately to obscure this anti-authoritarian holiday and assign it a new meaning ("Remembrance Day" throughout the British Empire and present British Commonwealth). Thereafter, anyone demonstrating against authority on that day would be easy to smear as un-patriotic.
It is not clear at all whether this outcome was a coincidence. A similar and deliberate strategy replaced May 1 with Labor Day to likewise deprive the communists of their own holiday, and make it possible to identify those who identified as communists vs. as unionists.
It is also a well-documented fact that the armistice was delayed some days simply "to have the war end on 11/11", which seems like a quite odd rationale that has never been fully explained. There is no obvious mystic significance to this date - but there was much anarchist significance, and perhaps the end of the terrible cost of that war was feared to bring on riots and politically empower anti-war forces, who would certainly have exploited a November 8 or 9 armistice effectively with an anti-government demonstration on November 11th, in the United States and Britain in particular. Moving the armistice a couple of days forward, of course, deprived them of this opportunity, and had the happy (for authority) side effect of permanently obscuring the anarchist holiday - which has never since been replaced with a comparable single date. This may reflect a lack of ability of anarchists to agree, however.
Most historians consider the struggle to assign a meaning to November 11 to be simply coincidence. Thus the coincidence status can play a role both in advancing, and defeating, any propaganda that is advanced based on synchronicity. If there is no real causal link, one is reduced to a rhetorical one.
See also: intimidation