The word “binding” means to “impose as an obligation.” So, the question is asking if people today are obligated to follow/obey the teaching of the Old Testament as they are obligated to follow/obey the teaching of the New Testament? Though the Old Testament is certainly just as true and factual as the New Testament since it was given by the inspiration of God, it is not true that it is just as binding today as the New Testament. The New Testament tells us the Old is no longer binding. The New has superseded the Old.
I do not know of anyone (who accepts the New Testament) that believes and practices that the Old Testament is just as binding as the New today. Some, however, do attempt to practice certain parts of it such as tithing and sabbath keeping. But I do not know of anyone who seeks to follow the Old Law regarding animal sacrifices, the burning of incense or the keeping of the Passover or Pentecost. There were some in the first century church who taught a convert to Christ must keep the law of circumcision. Therefore, the Lord points out, through the inspired apostle Paul, that when one seeks to obey even one part of the Old Testament Law (such as circumcision), he is obligated “to do the whole Law.” That is, those who teach circumcision as a religious ordinance or that one must keep the sabbath, must also burn animal sacrifices and keep the Passover. And, when one seeks to follow any part of the Old Testament Law, regardless of what it is, “ye are fallen from grace” (Galatians 5:3-4). Since men are saved by grace (Ephesians 2:8), those who seek to keep any part of the Old Testament cannot be saved.
One of the purposes for which Jesus came into the world was to nullify (abolish) the Old Testament Law by bringing in a New Testament Law. By Jesus dying on the cross, he abolished the Old Law — “Having abolished in his flesh the enmity, even the law of commandments contained in ordinances…” (Ephesians 2:15; cf. Hebrews 7:18). “Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross” (Colossians 2:14). Jesus, our saviour, is the mediator of the New Testament, not the Old (Hebrews 9:15). The whole point of the books of Galatians and Hebrews is to show the changing of the Law from the Old to the New. We will be judged by the words of Jesus in the New Testament (John 12:48).