The 1960s were an era of counter-cultural movements, meaning that all artists, be them musicians, painters, movie makers, strove to fight the culture that was pervading America at the time - mostly the Vietnam War and a corrupt government. Musicians especially talked about political affairs in their songs and reflected the spirit of the era - artists such as Bob Dylan, Leonard Cohen, and other were particularly vocal about their opinions on the topic. This was also a hippie era, when music was all about peace and happiness - so there were two opposing musical currents at the time.
Yes because if we did not have those laws in place, anyone could vote. Would you think its okay to let a 15 year old vote? Personally, i believe it would be good, but also illegal.