The Me 262 seems to have had a particularly large volume of fuel, which means a large volume of tank area to protect and a large target area. About 2,000 L (440 imp gal; 530 US gal).
This is 3-4 times the amount of fuel carried by say a Me 109 or Mustang. Perhaps it wasn't so much as vulnerable as more likely to be hit, in the manner of modern aircraft with little empty space.
I presume they were no more flammable than other types and had self sealing tanks typical of German aircraft: about an inch of rubber lining that expanded when wet by fuel to seal of the tank. It could perhaps accept a few stray 0.5 caliber rounds or absorb the external burst of a single 20mm round.
I presume one is relying on a damaged tank sealing itself so that there is insufficient fuel and inadquet air fuel ratio to sustain a fire. The tank can tolerate a few rounds but not too many. I imagine 1-3 might be fairly safe.
It should slow down the progression of a fire sufficiently for the pilot to get out. I would think that putting an ejection seat into the Me 262 such as that on the He 162 would be a priority.
One of the early decisions taken by Junkers was to run the engine of diesel fuel for the sake of economy and
safety, it was hard to synthesize high octane gasoline but diesel and kerosene like fuels which are linear chains are much much easier. In fact the Me 262 was multifuel: it ran of diesel grade called K2, a specialist jet fuel the Germans developed called J2. Some Me 262 missions were flown on crude oil only that had been refined by passing through a centrifuge only. The fuel was simply preheated and pumped aboard. (Germany and Austria both had some oil wells, but they were not suitable for producing aviation gasoline due to their low quality). Typically German aviation fuel at the end of the war came from distillation of coke, the benzol process from coke or by steaming of coal (Kerrick process) the fischer-tropsch plants and hydrogenation plants had been severely curtailed by bombing.
Nevertheless diesel fuel is safer than gasoline. I expect the J2 jet fuel was really the scum left over from diesel and gasoline refining and perhaps not as safe as diesel.
Incidentally Frank Whittle chose kerosene because of its resistance to freezing (unlike diesel which thickens) and safety.
BMW had chose to use low grade gasoline to fuel its engines, certainly B4 and perhaps the training aircraft A4 77 octane. The German air ministry found the convenience of using diesel/crude style fuels compelling and ordered BMW to make its engine compatible. The need to re-engineer the fuel system completely greatly delayed the BMW 003.
The Jumo 004 engines of the Me 262 were built around a solid magnesium casting (which helped align everything) while the compressor shell was also a fairly solid item. The rest of it such as the combustion chambers and exhaust duct was sheet metal though if a 0.5 inch hit a combustion chamber I doubt it would pass through the casing but destroy only once chamber. The engine might be shut down to contain a fire, the Me 262 apparently flew well on one engine so long as speed was kept up to maintain rudder authority. I'm not sure of what single engine max speed was but using a square law for 50% thrust loss one would expect 70.7% speed which is about 375mph: perhaps enough to dive away and disengage. There was thus a degree of twin engine safety.
One last note: Me 262 had steal frame baskets that could be placed over the engine to prevent humans from being sucked in, as a safety item, it turns our the aircraft performance was unaffected by these baskets and flown in combat to protect against debris.
The ground attack version of the Me 262 presumably had considerably increased armor as was the manner of ground attack versions of German fighters.
The Luftwaffe was particularly concerned with protecing its aircraft, that is why the new generation of fighters was to have flush side intakes with the air drawn in using boundary layer suction. A wind tunnel model was built and tested fine, the compressor drew 200hp from the turbine shaft. It also helped area ruling.