Bob Dylan had 7 US Top 10 records in from 1962-1970. He was a genuinely popular performer in and after the 1960s. However, as early as 1964 Dylan was distancing himself from his "protest singer" image, saying "Me, I don't want to write for people anymore - you know, be a spokesman. From now on, I want to write from inside me ...I'm not part of no movement... I just can't make it with any organization..." Most of Dylan's music that could be considered "activist" came from his early records which never broke the Top 10.
Actually, it's almost a cliche among both leftist activists and music critics to compare the respective careers of Dylan (who wrote about a lot more than politics, and generally couched his political expression in poetic, often historical metaphors), and Phil Ochs (who was widely known and admired, at least by leftists, at the time, but whose songs tended to be far more topical and directly address contemporary political issues). One of them is a household name today, one is a footnote, and there are many debates about exactly why that is, although there's a broad consensus that Dylan's songs are much more relatable to people who don't know the detailed political context necessary to grasp a topical song.
Here are the Billboard top selling #1 albums and top 100 singles of the 1960s that can be considered 'activist' in some way:
Top 100 singles
1962
1963
1965
1966
1967
1968
1969
#1 ALBUMS
1962
1963
1966
Many of the top selling acts of the 1960 were politically outspoken, such as Peter, Paul and Mary, Joan Baez, Bob Dylan, Jefferson Airplane, The Beatles. Sometimes this reflected in their music, sometimes not. But there were also more subtle things at play, like having long hair, having an Afro hair style, espousing the power of love, druggy lyrics etc. could be considered a political acts, that undermined the "system"