What features enable the Su-25 Frogfoot to operate with such a wide variety of fuels?
Being a ground attack aircraft, the Su-25 has an operational ceiling of 23,000 ft and will not encounter the low temperatures to which a Boeing 777 is regularly exposed. Therefore, the risk of diesel fuel gelling and clogging the fuel lines is much lower.

On the other side of the temperature scale, gasoline could vaporize in hot environments and equally endanger the fuel supply of the engines. Those extremes are rarely found in the countries of the former Eastern Bloc, and the Su-25 was primarily designed for operations in moderate climates.

Nevertheless, some modifications are advised in order to avoid trouble when exotic fuels are used:


Regular fuel pumps use kerosene for lubrication. Kerosene is a good lubricant and allows for a simpler pump design. By using better bearings, the fuel pump can also be used with gasoline or petrol without suffering long-term damage.
Running the fuel lines away from hot surfaces reduces the risk of vapour bubbles forming inside. I don't know the details of the Su-25 design, but I would be mightily surprised if any fuel line runs right below the upper skin of the aircraft where the sun can heat the surface to temperatures in excess of 70°C even in moderate latitudes. This is supported by a light grey paint scheme as shown by the Ukrainian Su-25 in your question.
Don't do fancy things with the fuel, like use it as a hydraulic fluid, but restrict its use to being burned in the engine, and maybe cool some engine oil on its way into the combustor. Then any liquid hydrocarbon can be used.


That turbofans can run on a wide variety of fuels has been established in the answers to this question.