I think that it is too bad that we cannot hear the inflection in Jesus' voice when He spoke this. I wonder if maybe there was not an ironic cast to what He said. Or, should we be so bold as to say that maybe there was some sarcasm here? I mean, "They sit in Moses' seat!" The reason that I ask is because there is evidence that the Jews of His day (in Jesus' day) called the seat from which the leading rabbi of any synagogue—not the chief synagogue, we might say, in Jerusalem; but any synagogue—they commonly called it "Moses' seat." And so there were "Moses' seats" all over the nation.
In addition to that, the grammar here indicates that the phrase ["sit in Moses' seat"] could have been translated that they "sat down," or (to make it a little bit plainer) "have seated themselves." Or, (even more forcefully) "have presumed to sit" in Moses' seat. All of which can lead one to ask whether their authority was truly real, or rather was it was something that they had grasped at when the occasion arose for them to take it?
Is Jesus telling us that we should obey everything the religious leader tells us? That cannot be. Remember that Jesus was the one who told His disciples to "Beware the leaven of the Pharisees." (That's in this same book: Matthew 16:12.) That leaven, the context shows very clearly, was their doctrine. He said to beware of what they were teaching. And yet it appears to say here that whatever they tell you to do, that you should do. No, we are not to do everything that they tell us to do.
Jesus' own life was an example, and He did not do that. He did not do everything the religious leaders of His day said to do—not in the least! He frequently had confrontations with them. He was accused by them of breaking the Sabbath, and in turn, He told them that they were of the devil. In addition, right in the context, He showed that the fruit of their lives cast suspicion on their teaching.
So, He's not telling us that we should obey everything that they say. He is telling us that we are to obey what they tell us that is in agreement with God's Word. That we should obey. However, even if what they say in their teaching is wrong and we cannot obey it, we are still subject to them if, indeed, they are the human authority. Jesus Himself followed that responsibility. He lived well within the limit of His authority.