There is no doubt that the Jews were a religious people. There is no doubt that they were attending synagogue. There was no doubt that they were looking into things in the Bible. There was no doubt that they were talking with one another—even as people today, in this nation, talk to one another about religion. They go to church on Sunday, or on Sabbath, or maybe on Friday. We are a reasonably (or, fairly) religious people; but I think that you would have to agree with me that it is not according to knowledge. Same thing with the Jews back in the time of Christ, back in the time of the apostle Paul, and both before and after those times, as well.
"Ignorant" does not mean that they were stupid. It simply means that they were uninformed. They did not know. They had no knowledge of, no grasp of, God's righteousness.
They were ignorant of God's righteousness. Righteousness simply means "right doing; rectitude." According to Psalm 119:172, righteousness is defined as the commandments of God. That is right doing! So we see here that, by definition, these people did not know of God's right doing—God's right way, God's right method, God's commandments. We see that confirmed in Mark 7, where Jesus said:
He said that about the Jews. The Jews went about and they established their own standard, their own forms of righteousness, and their own religion—called today "Judaism" (called in the King James Bible "the Jews' religion"). The Jews' religion was not the religion of God. It had bits and pieces and parts of it; but it did not exemplify the right and the true way of God at all.
That is why there is so much disagreement between Christ and the Pharisees and the Sadducees. There they were—the religious leaders—representing the way of Judaism, and Christ called them into account for the things that they were doing.
So that pretty well summarizes it—that is, the standing of the Jews. I do not mean, in any way, to put them down. God simply was not working with them. He was not attempting to convert them. He called out a few here and there. There was always "a remnant" that was doing the truth of God, but, by and large, those in the public eye—those who were setting the standards; those who were leading the great bulk of the people—were not the ones that God was working with. They were the ones who "left the record." They were the ones who did the bulk of the writing, but their writings did not agree with the Scriptures of God.
The apostle Paul was just as much a victim of the deceptions of Satan as we. He, too, had to have the "scales" lifted from his eyes, so he could see the truth of God.
Now that sums it up, I think, about as well as any series of verses in the entire Bible. We cannot trust the record—the tradition—of the Jews in regard to spiritual things because they were just as unconverted as we were.
So, we see a summation here in Romans 10:1-3, that the Jews are not to be trusted any more than any other people in regard to spiritual things. They had erected a system of worship that is called Judaism; and, oh, it was strict. Oh, they were zealous for it; and, oh, it was done in the name of God (just like "Christianity" today). But this religion was in agreement with their own character—not the mind of God! We have just seen the witness of that in God's Word. They were not in agreement with God. Some were doing things right, but the vast majority were not—even as it is today.