Bob Dylan – The Times They Are A-Changin' lyrics

I think its about the change that hippie movement was attempting to bring about. He was urging people(politicians, parents, the media) to not judge the ideals of the youth.
Some people(the media, parents) saw the hippies as troublemakers and were fearful of how big this counter-culture was growing. The government saw them as socialist-pacifists that were becoming the biggest cultural phenomenon ever and feared they could become a threat to oppressive capitalist society and states such as the us and uk; much like the British saw meetings of revolutionaries during pre-revolution America as a threat to British control over the colonies.
Dylan begging for people not to fear the change.

It is about the Civil Rights Act of 1964. The Civil Rights Act of 1964 (Pub.L. 88–352, 78 Stat. 241, enacted July 2, 1964) is a landmark piece of civil rights legislation in the United States that outlawed discrimination based on race, color, religion, sex, or national origin. It ended unequal application of voter registration requirements and racial segregation in schools, at the workplace and by facilities that served the general public (known as "public accommodations").
He's calling on the Senators and Congressmen to not stand in the way of this landmark legislation.
"Come senators, congressmen
Please heed the call
Don't stand in the doorway
Don't block up the hall"

This song predates (or was, at least, at the beginning of) the hippie movement - written around '64 or 5. But Dylan was a visionary/poet. He ran with the East Coast radical singers and songwriters of his time. He was in an on again, off again relationship with Joan Baez and may even Predate his time at" Big Pink" - a shared house and recording studio in upstate New York.

The times today are similar. In the sixties there was a war which was only defending the wealth of the wealthy. The draft was rigged so by policy the sons of the poor were the first to be called. Now, the poor has to go in order to have an income. Back then the movement made the government eliminate the law of the draft. The youth was united in purpose even the children of the wealthy had a sense of morality. Not so today. The children of the wealthy has adopted the greediness and lack of love of their wealthy parents. So, the song is only for those who understand what it is to have love of fellow man and love of country disregarding the love of money. There was more benevolence in the sixties than today. What is great about today is that there is power in numbers. 20% controls 93% of the financial wealth by policies that distribute the wealth of the country obscenely unfairly. The bottom 80% shares only 7% of the wealth. But they are still 80% of the population and that is a big number. And they are waking up. The government have no power this time because we have allowed wealth to have more. Abraham lincoln's prophesy came true.
"i see in the near future a crisis approaching that unnerves me and causes me to tremble for the safety of my country. .. Corporations have been enthroned and an era of corruption in high places will follow, and the money power of the country will endeavor to prolong its reign by working upon the prejudices of the people until all wealth is aggregated in a few hands and the republic is destroyed. "
-- you. S. President abraham lincoln, nov. 21, 1864.
(letter to col. William F. Elkins).