Acts 15 famously records what parts of the Jewish law is considered binding on non-Jewish Christians:
28 For it has seemed good to the Holy Spirit and to us to lay on you no greater burden than these requirements: 29 that you abstain from what has been sacrificed to idols, and from blood, and from what has been strangled, and from sexual immorality. If you keep yourselves from these, you will do well. Farewell.”
One will note that the Sabbath day laws are not part of this. As such, the direct answer to your question is thus: At the Council of Jerusalem, c. 50 AD. Over the course of the first few centuries, Gentile Jews (not subject to the Sabbath laws) came to outnumber Jewish ones, establishing the custom for all.
The Why, of course, stems from Jesus' example and teaching. Understanding Do we have to obey the laws of the bible? If so, what laws? is key to this - and the summary is as follows:
In Mark 2, Jesus was asked precisely this question - Why do your disciples "work" on the Sabbath. The text reads:
23 One Sabbath he was going through the grainfields, and as they made their way, his disciples began to pluck heads of grain. 24 And the Pharisees were saying to him, “Look, why are they doing what is not lawful on the Sabbath?” 25 And he said to them, “Have you never read what David did, when he was in need and was hungry, he and those who were with him: 26 how he entered the house of God, in the time of[d] Abiathar the high priest, and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and also gave it to those who were with him?” 27 And he said to them, “The Sabbath was made for man, not man for the Sabbath. 28 So the Son of Man is lord even of the Sabbath.”
His answer, that the Sabbath was actually made for man - to be a rest, and a joy - illustrates the "point" that the law is there to help, not to hurt. For example, in Luke 14 it says:
14 One Sabbath, when he went to dine at the house of a ruler of the Pharisees, they were watching him carefully. 2 And behold, there was a man before him who had dropsy. 3 And Jesus responded to the lawyers and Pharisees, saying, “Is it lawful to heal on the Sabbath, or not?” 4 But they remained silent. Then he took him and healed him and sent him away. 5 And he said to them, “Which of you, having a son[a] or an ox that has fallen into a well on a Sabbath day, will not immediately pull him out?” 6 And they could not reply to these things.
As a matter of course, the New Testament is pretty clear that for Jesus "rules" are less important than relationships. The concept of grace is fairly central to most Christian understanding of how "right action" before God is to be considered. At the risk of sounding antinomian, Christians who rely on grace do not see the "law" as the point, but rather the means. As such, working on the Sabbath is not a "most important thing" when it comes to living life.
(Oh, and of course as Seventh Day Adventists would point out, the Sabbath is Saturday anyway.)