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No. Richard Nixon is the only president who voluntarily left office before the end of his term. Every other president left office after choosing not to seek another term, being defeated in an election, or dying in office. There are several presidents who were elected and served one term then were defeated in the next election (Adams, Q. Adams, Pierce, Hoover, Carter, etc.), but none of them can be fairly characterized as having been ‘protested out of office.’
The closest that the US ever came to protesting a president out of office would have to be Nixon’s immediate predecessor, Lyndon B. Johnson. Johnson became president in 1963 after the assassination of John F. Kennedy. During his first term (from 63-64, finishing JFK’s term), he had remarkably high approval ratings (an average of 74% according to gallup)). He succeeded in passing the Civil Rights act, then was re-elected in 1964 one of the most lopsided elections in American history. His second term included passage of the voting rights act along with the war on poverty embodied by the great society programs. However, he also began American involvement in Vietnam. By 1968, mostly as a result of the war, Johnson was deeply unpopular with the Democratic party, which was in the process of tearing itself apart. As he had taken over from Kennedy more than halfway through his term, Johnson was still eligible to run for re-election. Due largely to the unpopularity of Vietnam, he was challenged in the Democratic primary by the anti-war Eugene McCarthy. Although he won the first primary (in New Hampshire) McCarthy had a relatively strong showing, which demonstrated Johnson’s electoral weakness to the rest of the party. Seeing this, Robert Kennedy entered the race 4 days later. Realizing that he had no realistic path to victory, Johnson withdrew from the race on March 31, 1968.
As for Nixon, he left office ‘voluntarily,’ choosing to resign rather than be forced out by impeachment. Although there were frequent protests against Nixon during his administration (again largely due to Vietnam), he maintained high popularity for most of his time in office and was re-elected in 1972, winning with 60% of the popular vote and an electoral college margin of 520 to 17. Nixon’s popularity did not collapse until the full scope of Watergate came to light. After the congressional hearings in May 1973, his approval ratings collapsed into the 20s and never recovered. It is important to note that while the late 60s and early 70s are often remembered for being times of significant protests and counter-culture movements, it was still counter-culture. I.e. it often represented the views of a disproportionally loud minority. Nixon understood this and was able to use protests against him as a wedge issue to motivate his base. He coined the (frequently misused) term ‘silent majority’ to represent this division. The silent majority was the large group of Americans who supported the war and did not protest.
Sources / recommended Reading for Nixon and Johnson:
All the President’s Men Woodward and Bernstein’s account of the Watergate investigation