Short answer:

We were at war with Fascist Italy, but not with Spain: big difference. Spain's position during the Second World War is complex; not perceived as an enemy by the Allies. Perhaps a bit like Sweden, Spain was a "complicated neutral power".

Discussion:

Spain was ostensibly, and in some practical ways was actually neutral (though "leaning" Axis) during the Second World War. True, Spanish volunteers (some more voluntarily than others) had fought under German command on the Eastern front, but Spain was incentivized to stay officially neutral, and then as the war went on, began to tilt away from Germany. Even while the Blue Division was fighting at Stalingrad, Franco refused German requests to permit German military forces to transit Spain to attack the British fortress at Gibraltar-- a position that was of great value to the allies.

An alliance which was trying to establish a more orderly, peaceful world had little cause to go to war with a neutral power to replace its government, and the US in particular itself had a history of "volunteers" during its period of pre-war neutrality (the Flying Tigers, for example). Britain and the US didn't have that much bad blood with Franco, and he took steps as the war went on to accommodate American and British concerns.

Quite recently, previously classified documents have emerged which suggest that during the War, British intelligence began paying Franco to stay neutral, or to be "more neutral", a wonderfully complex "game of spies" including large payments by MI6 through Ambassador Hoare in Madrid.

Beyond that, as the Cold War began, Franco's anti-communism fit Western policy. Planners were concerned about the possibility of communist victories in countries around the Mediterranean-- there was a civil war in Greece, with a narrow bloody victory by anti-communist forces, great effort was required in Italy to keep the left out of power.

In that context, Franco didn't look so bad to the US ; he offered the US military bases -- a large naval base in Rota particularly important. Franco also cooperated in a set of policies to demonstrate a commitment the removal of Nazi influence over the regime, this process began during the War, as Franco saw the tides turn against the Axis.

So, for example, Spain signs an agreement on May 2, 1944 with Britain and the US, to restrict sales of tungsten to Germany, and to deport German intelligence agents. This agreement marks the beginning of a complex and graduated diplomacy by the Franco regime to get Spain in line with the coming post-war order-- one can say that the regime was rather skillful in this regard.

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See:

MESSENGER, DAVID A. “Beyond War Crimes: Denazification, 'Obnoxious' Germans and US Policy in Franco's Spain after the Second World War.” Contemporary European History, vol. 20, no. 4, 2011, pp. 455–478.

Caruana, Leonard, and Hugh Rockoff. “A Wolfram in Sheep's Clothing: Economic Warfare in Spain, 1940-1944.” The Journal of Economic History, vol. 63, no. 1, 2003, pp. 100–126.

"Spanish Neutrality: Release of Blocked Funds" FO 1093/233 [British Foreign Office File] 5 June 1940 - 31 December 1941; available online here