In the days when ships were steam powered, fuel requirements were less onerous and a lower grade of refinery product could be used.  That was known as "furnance fuel oil" in the Commonwealth navies, not sure what it was called in the USN, and that would have been pretty universal around WW2.  Steam ships could, with minor mods, burn ADO/MGO/F76 and in the last years (after about 1960) many did.  One of the reasons the Brits gave for not sending Britannia to the Falklands as a hospital ship was that she, alone, of the task force would still have required FFO.  However, from my experience elsewhere FFO was still widely used at that time!

There was considerable diesel presence in WW2 (and WW1 for that matter).  All WW2 submarines, many coastal craft and sweepers and lots of merchant ships used diesels and the fuels that they used would almost certainly be OK for modern diesels; and they would definitely be usable by GTs.