The statement ""Blowin' in the Wind" and "The Times They Are A-Changin'" became theme songs for the counterculture because their messages supported civil rights and protested war," is true.
"Blowin' in the Wind" is a song that Bob Dylan wrote in 1962 and released on his album The Freewheelin' Bob Dylan in 1963. Blowing in the wind is a song intended to and it deals with peace, war, and freedom.
"The Times They Are a-Changin'" is a song which author is Bob Dylan and was released as the title track of his 1964 album which has the same name.