Why doesn’t the Church of Jesus Christ of Latter-day Saints keep the Jewish feast days? The Apostle Paul stated in Acts 18:21 that he had to keep the keep the feast that was coming to Jerusalem. In Acts 20:16, Paul is very adamant about being in Jersusalem for Pentecost. Why would he need to be in Jersusalem for those days unless he intended to keep the Jewish holy days? If the Apostle Paul kept those holy days, wouldn’t the Saints today do so?
The Jewish holidays, including the feast days, were a part of the law Moses brought down from Mount Sinai. We believe all such things were fulfilled in Christ, so there is no longer a religious reason to observe the feast days or other holidays.
Paul was a Jew by birth and by culture, and his ministry was initially among the Jews. As a Jew, Paul would have wanted to observe the religious holidays if possible. He had a further interest in being in Jerusalem at Passover because he wanted to preach to the Jews. Read Acts 21 for the effect of this preaching.
In addition, it’s entirely possible that neither Paul nor the other apostles were yet aware that the fulfillment of the law of Moses meant that the religious holidays were no longer required. Such knowledge came line upon line, not all at once.
The bottom line is: Latter-day Saints do not observe the ancient Jewish holidays, because we have not been instructed to do so by our leaders. If the Spirit were to move our leaders to tell us that such observance was important, we would certainly begin observing them.