“The Catholic Church rejects nothing that is true and holy in these religions. She regards with sincere reverence those ways of conduct and of life, those precepts and teachings which, though differing in many aspects from the ones she holds and sets forth, nonetheless often reflect a ray of that Truth which enlightens all of humanity.” (NA2) What is important about this statement from Nostra Aetate? What does it mean for how we treat those of other religions? Why does respecting people of other religions matter to us still today, more than fifty years after the promulgation of this document?

What is important about this statement is that it marks a change in the Church's stance towards the adherents of other religions. The statement itself opens the door for the Catholic faithful to pursue mutually satisfying relationships with people of other faiths, notably those of the Jewish faith.
The document itself (although 50 years old) paved the way for an improvement in Catholic-Jewish relations. It argued that, although "the Jewish authorities and those who followed their lead pressed for the death of Christ," all Jews should not be held responsible for the execution of Jesus Christ. The Nostra Aetate also recognizes the contribution of Hindus, Buddhists, and Muslims to matters of faith. It accepts that these three religions understand the "radical insufficiency of this changeable world" to satisfy the yearnings of the human soul. 
The tenets enshrined in the Nostra Aetate are a radical departure from the traditional Catholic theological stance. Its importance cannot be underestimated, as its publication inspired a similar Jewish document called Dabru Emet: A Jewish Statement on Christians and Christianity. The Dabru Emet acknowledges the common spiritual heritage both faiths share. Just as the Nostra Aetate reverses centuries of Catholic animosity towards Jews for the crucifixion of Christ, the Dabru Emet acknowledges that "Nazism was not a Christian phenomenon" and that only God can ultimately settle the irreconcilable spiritual differences between Jews and Christians.
So, respecting people of other religions is as important today as it was more than fifty years ago because it fosters peaceful coexistence in an increasingly volatile world.