Ignoring the technicalities and assuming ASB: Almost no strategic effect (probably).
The P51 was a great escort fighter due to its range, it wasn't systematically better than its peers in other dimensions, so I'm going to look at the effects of longer range but equivalent performance fighters in other periods with no overall increase in fighter numbers.
1940: I don't see it having much effect since the Allies were operating on the defensive. It is possible that it might have been used as an escort in the daylight raids in 1939/early 1940, but while this might reduce bomber losses it would raise allied fighter loses, both with very minor effects
1941: RAF fighter operations over France are at less of a disadvantage, but the German defenders retain the initiative and it doesn't have much effect. A radical (and unlikely) change would be to shift bomber command to daylight raids escorted in force by fighters. This would impose heavier losses on the German fighter force by attacking targets they want to defend, forces the Germans to withdraw fighters from other fronts. However, the British are unlikely to commit sufficient fighters to this campaign to inflict real damage on the luftwaffe. This is because the British wanted to preserve fighter command in case of Russia being defeated and the Luftwaffe returning to the West, so in this case fighter command losses might be similar and German losses higher than actual but bomb damage inflicted is likely to be similar (ie trivial).
1942: similar to 1941, the fighter command just does not have the strength to defeat the Luftwaffe, although it can impose heavier losses and force units to be withdrawn from other fronts.
So up to this point German losses are a bit higher but Germany has a better daylight air defence system and has probably produced more fighters and fewer bombers than in OTL. The net effect of a little less air support in the Med or on the Eastern Front is probably small.
1943: Fighters are available to properly escort the US 8th air force from the start, but this is where my assumption of no extra fighters starts to really limit the impact. As in the earlier years there are unlikely to be sufficient fighters to impose crippling losses on the Luftwaffe until Autumn/Winter and at this point the weather intervenes. It's important to understand that the Luftwaffe was suffering increasingly unsustainable losses throughout the 2nd half of 1943 The importance of the P51 here was psychological as much as anything. Being able to escort the bombers throughout their mission reduced their losses, raised their morale and gave strategists confidence in the plan. The relatively small number of P51s employed in escorting the bombers at the furthest extents of their journey saved some bombers and inflicted some losses but wasn't critical. They did allow the US to raid more distant targets than would otherwise have been the case but again this probably wasn't critical.
There are a few hypotheticals that I think are interesting
1. Salerno was chosen as the invasion beach in Italy because it was just within spitfire range (it turned out to be too far really). What if longer ranged fighters lead instead to a landing near Anzio? Given longer flight and shipping times this means less air support and a slower build up, so the landing is more likely to be defeated, but if successful it accelerates the Italian campaign by about 8 months.
2. What if Fighter command is fully committed to long range escorting of the 8th Air Force from the start of 1943? Fighter command might have been able to inflict similar luftwaffe losses to those the 8th air force inflicted in the spring of 1944 but a year early. US bombing is unlikely to inflict much more damage on German output than OTL, although if bomber command switches to daylight bombing this could change (but is unlikely). From 1944 the luftwaffe was still able to gradually build up a reserve to use on specific operations, but of decreasing quality, and this is likely to be the case with higher losses in 1943. The allies generally had significant air supremacy from the 2nd half of 1943, this change might bring this forward in time and make it greater in degree, but neither are likely to bring the war to an earlier end. Essentially airpower was critical for victory but was not sufficient.
3. DDay was in Normandy because it was within spitfire range, as with Salerno longer range fighters enable a wider range of invasion locations to be considered. However, given build up requirements and the coastline it's not obvious to me that there is a better alternative, although the Germans might have had to disperse their troops more widely
