Yes and no. First, some context is necessary. The McCarthy era was a very contentious time in American politics. While Senator Joseph McCarthy and most of his supporters were Conservative Republicans, there were also a few conservative Democrats who bought into the Cold War idea that there were traitors and secret Communists everywhere. The HUAC began investigations, the government began requiring loyalty oaths, and deep suspicion dominated the country. Meanwhile, moderate Republicans and Democrats were put in a difficult position: if they objected to McCarthy's methods or tried to demand proof to support his allegation that hundreds of Communists had infiltrated both the US government and Hollywood, they were immediately accused of being "soft on Communism." So, for a while, even those who disliked McCarthy or thought he was conducting a partisan witch hunt kept silent, as hundreds of people (most of whom turned out to be innocent) were brought before the HUAC and accused of being Communists.
Ultimately, the journalist Edward R. Murrow was one of the few who spoke out against McCarthy and successfully refuted his claims; McCarthy gradually lost his grip on power, and then, finally, in 1954, members of the Republican party censured and removed him. History has since shown that McCarthy's assertions were too often false or exaggerated, dangerous political rhetoric aimed at people whose political views were to the left of his. As a result of his accusations, many of the people who were called before the HUAC lost their jobs or their reputations, simply because McCarthy and his allies had said these people were Communists, or Communist sympathizers, and the public seemed to believe that he wouldn't accuse them if there weren't a good reason.
That said, yes HUAC did find some people who were adjudged as Communist sympathizers or Communist spies. One high profile Communist was a government employee named Alger Hiss. Also convicted were the "Hollywood Ten," liberal film directors who may or may not have had Communist sympathies but who refused to cooperate with the committee (which they believed was violating their freedom of speech and freedom of association) and were then sentences to prison for Contempt of Congress. Julius and Ethel Rosenberg were also found to be Communist spies (and sentenced to death), although later documents from the so-called Venona Project seemed to exonerate Ethel, while proving Julius was in fact guilty. There were a handful of others as well whom the HUAC investigated and determined to be Communists. But the number was far smaller than the hundreds (perhaps thousands) of people whose lives were ruined by false accusations, at a time when belonging to a left-wing organization or reading magazines considered pro-Communist were enough to get someone in serious trouble.
It should also be noted that to this day, there are still some political conservatives who sincerely believe the government and Hollywood were in fact dominated by Communists; they seem to agree with McCarthy's belief that anyone who belonged to a left-wing organization was by definition pro-Communist. This view persists even today, as some political talk show hosts regularly accuse liberal Democrats of being Communists (a charge also made in 2012 by a Republican congressman named Allen West). And a related controversy broke out in Texas in 2009, when conservative Republicans on the Texas State Board of Education wanted history teachers to instruct students that McCarthy was a hero for having found and driven out thousands of disloyal Americans. They claimed the Venona Project proved McCarthy was right, but scholars have noted the Venona files are often fragmentary and contradictory, and do not "prove" anything. Further, most objective research about the "Red Scare" and McCarthy has repeatedly shown that his accusations were based more on political ideology (ultra-conservatives vs. ultra-liberals) rather than on documented facts. Yet the controversy about whether McCarthy and the HUAC were positive or negative persists.
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McCarthy accused many Americans of being communists. Ironically, he was never able to actually identify any communists. People who McCarthy named were brought before a senate committee and made to testify, and try to explain their innocence. McCarthy ruined many careers by falsely accusing people of being communist.
Communists
Andrew Jackson
There's no record of it ever happening, so no.
If you're asking whether any US Presidents were constitutionally ineligible to hold office, the answer is no.