The change to the pledge was part of a broader movement over the past decade in the United States to distinguish Americans from "godless Communists" during the Cold War. There was a rise of civil religion—church attendance and profession of belief in general Christian principles tied closely to one's American identity. Which denomination one might attend was far less important than just believing at all; it wasn't, in other words, a competition over theology, rites, or practices.
Billy Graham rose to fame beginning in 1949, a symbol of this notion of civil religion. He frequently denounced Communism and intertwined American democracy with Christianity. Prior to this time, the phrase, "under God" was used sparingly by American politicians and presidents. But it was Truman who began to use it more frequently, and like Graham, it was often used to denounce Communism.
The Pledge of Allegiance wasn't the only thing that was changed. It was during this time that the phrase "In God We Trust" was added to paper money. The phrase was also added to the speaker's dais in the House of Representatives, and above the entrance to the US Senate chamber. The National Prayer Breakfast became a larger part of American politics. These movements were often spearheaded by fraternal organizations. It was the Knights of Columbus that pushed to have the pledge amended with the phrase, "under God." Another organization, the Fraternal Order of Eagles, worked with American director Cecil B. DeMille to place monuments of the Ten Commandments across the country. DeMille's film, "The Ten Commandments," was coming out in 1955 and so he readily partnered with the Eagles to have the monuments—monuments that in the last thirty years have been the subject of several court challenges—placed on public land, both because he believed in their mission and because he saw it as an opportunity to promote his film.
In other words, the changes to the pledge were just one part of a sharp focus in the late 1940s and 1950s on publicly demonstrating, both as a nation and as individual citizens, one's commitment to God, religion, and America. Historian Kevin Kruse has also written about the role of businesses and the capitalist angle in the shift (Kruse, "One Nation Under God: How Corporate America Invented Christian America) that is excellent.
There was minor push back on these changes, but nothing that made a dent or gave pause to the shift. Some Jewish organizations wrote letters of protest. There were, of course, actual Communists in the United States as well as atheists who also spoke out, but that was the extent of the protests: speaking out. No large, well-organized or well-funded campaign emerged to offer legal challenges.