A shared origin, by this account
Fomenko and Nosovsky argue that the crescent paired with a star or cross was originally a single, shared symbol across a much larger historical empire, later dividing into the crescent-and-star now associated with Islam, the cross retained by Christians, and the six-pointed star associated with Judaism. As a supporting example, they note that a crescent was displayed atop St. Stephen's Cathedral in Vienna until it was removed in 1685, after which it was preserved as a relic in the city's museum — evidence, in their reading, that the symbol was not originally an exclusively Islamic one.
Examples on Russian coats of arms
The authors catalogue a number of historical Russian city and provincial emblems combining a crescent with a cross or star, including those of Borzna, Konotop, and Zenkov, in what is now Ukraine, and Belozersk, in the Novgorod region, several dated to the late eighteenth century. They also describe the coat of arms of Kostroma province, which depicted a crescent and cross and which, in their account, was ordered restored by decree under Tsar Paul I in 1797 and again under Nicholas I in 1834, before finally being dropped in 1878.
How this argument is used
Fomenko and Nosovsky present these examples as part of their broader "New Chronology" theory, which proposes a substantially revised account of medieval Russian and world history and departs sharply from the timeline accepted by mainstream historians. The crescent-and-cross examples described here should be read as evidence marshaled for that specific, disputed theory, rather than as an established historical consensus about the symbol's origins.