This is kind of complex.

You see, race is a social construct, and in Latin America it was seen much differently than it was in the United States during the 50's. The Casta system, which was leftover from the colonial era, has informed the way race is perceived in Latin America for centuries. If you want to boil it down, the more purely European you were, the more privileged you were, with actual Europeans at the top (españoles), followed by descendants of Europeans born in the colonies (criollos), mixed European and indigenous (mestizos), and finally indigenous peoples and African slaves. There were also various other classifications, but this covers it in general.

Being a Spaniard or criollo typically provided you with access to wealth and privilege beyond what other classes could achieve, with some exceptions. One by one, Latino nations threw off the formal caste system, but its residual effects could be seen in the wealth of the criollos well into the twentieth century in much of Latin America.

Of course, the claim to racial purity tended to be bogus, as most such claims do. Most criollos had some indigenous ancestry, and many mestizo families that achieved wealth married into criollo families. However, criollos did appear white, which was very important to the people at the time.

And here we have Desiderio Alberto Arnaz y de Acha III. If you could not tell by his name, he was a criollo. More importantly, he was a criollo with a fabulously wealthy family. Even more importantly, he was a famous criollo with a fabulously wealthy family. As far as Americans were concerned, he was acceptably white-ish. He was a bit risqué, but ultimately wealthy and foreign enough to make up for the vague hint of some nonwhite ancestry. People raised eyebrows when Lucille Ball married him, but neither was famous enough for it to cause too much of a stir.

That said, it absolutely caused a stir when Lucille Ball pitched I Love Lucy.

Some background: Both Lucille Ball and Desi Arnaz had already achieved B-list fame by the time they married. After WWII, Desi toured with his big band show while Lucille starred in several comedies back in Hollywood. Fearing that their marriage couldn't handle that stress, Lucille pitched the idea for I Love Lucy with her starring next to Desi, and CBS hated it. They were eager to sign her, but asking Desi to be in every living room in America married to a white, homegrown gal was too much.

Of course, Lucy was smart. She knew comedy, she knew she and Desi had chemistry, and she knew how to show that off. She and Desi went on the vaudeville circuit and basically proved that their chemistry overrode any misgivings their audiences might have about race, and they were able to win people over quite quickly.

In general, Americans were vaguely uncomfortable with Desi Arnaz being married to Lucille Ball until they saw the two of them together. It helped that their son looked and sounded like a white American.

EDIT: Oh, I missed the bit about the Cold War! Desi and Lucy married in 1940, so the Cuban revolution hadn't happened yet. I believe she testified before the House's Un-American Activities Committee, but nothing came of that. Desi's family was part of the upper class that was overthrown in the Cuban revolution, and they lost several estates and a lot of wealth, so no real suspicion ever fell on him, and he was vehemently opposed to Castro.