The Jews of Jesus's time were not particularly moral; they were particularly moralistic. They went to great lengths to put on outward appearances of piety, which repeatedly earned them the condemnatory epithet of "hypocrites!" from the Savior. We get a pretty good sense of what they were like from the Gospels. For example, using legalistic tricks to get out of caring for their parents by instead being able to (very visibly) donate the money to the temple, "and many such like things":
8 For laying aside the commandment of God, ye hold the tradition of men, as the washing of pots and cups: and many other such like things ye do.
9 And he said unto them, Full well ye reject the commandment of God, that ye may keep your own tradition.
10 For Moses said, Honour thy father and thy mother; and, Whoso curseth father or mother, let him die the death:
11 But ye say, If a man shall say to his father or mother, It is Corban, that is to say, a gift, by whatsoever thou mightest be profited by me; he shall be free.
12 And ye suffer him no more to do ought for his father or his mother;
13 Making the word of God of none effect through your tradition, which ye have delivered: and many such like things do ye.
Remember that by the end of Jesus's life, he'd become such an annoyance to the political rule of the various factions of Rabbis that they paid off a traitor to help apprehend him, explicitly sought for false witnesses to find a way to charge him, convicted him of blasphemy in a trial in which practically every point of procedure was illegal under Jewish law. Once he had been convicted of blasphemy, they wanted to put him to death, but only the Romans could enforce capital punishment, and as polytheists they didn't really have much of a concept of "blasphemy," so they had no compunction against hauling him before Roman authorities and changing his charge to the highest crime that Rome accepted: treason. When he was interviewed by the Roman authority (Pilate) and found not guilty, they pressured him and even threatened to have him charged with treason by higher Roman authorities if he wouldn't play along. (And historians suggest they'd have had a good chance of making the charges stick, so he had to give in to save his own hide.)
These were the people in charge of the "moral society" of Jews ~30 AD, making the rules and setting the example for the common people to follow. Not a particularly good example of moral people, in my opinion.
As for standing out as an alternative to the status quo, yes, that's true, but the other side of that is that Christianity requires repentance, which involves changing one's ways. It's one thing to say "wow, those Christians are really cool, I wish I could be like them," and another to actually sincerely try to give up all your sins, especially when it impacts your relationship with your friends and family.
29 And every one that hath forsaken houses, or brethren, or sisters, or father, or mother, or wife, or children, or lands, for my name’s sake, shall receive an hundredfold, and shall inherit everlasting life.
Jesus didn't say this just to sound cool; he said it because it was a very real possibility of what might be required in order to truly live the Gospel.