Answer: It's true that God forbade the Israelites to use, or even possess yeast (or leaven) in their homes during the 8 days of Passover and Feast of Unleavened bread. It's also true that yeast was biblically a symbol for sin. It became a valuable word-picture for the Jews in understanding the way sin can spread throughout our lives.
But it is untrue that Communion bread must be unleavened in order to be acceptable. I say this based on two important points:
1. It is incorrect to assume that the ceremonial requirements for Israel's worship observances transfer to the Church.
Many Christians assume that Old Covenant regulations and prohibitions carry over to the New Testament Church. As you can imagine, this has resulted in huge and long-lasting debates: Should we still worship on the seventh-day Sabbath? What about requirements for clothing, or food laws?
It is vitally important to remember that, as the Body of Christ, we are not under the Mosaic Covenant and the ceremonial regulations given to Israel are not in force for the Church.
2. There is nothing in the New Testament that suggests Communion bread must be unleavened.
Yes, Jesus and His disciples would have eaten unleavened bread during the Last Supper, but that's because they were observing Passover. We must remember that Communion is not a recreation of Passover. It is a remembrance of Christ's death on the cross. Therefore the requirements and prohibitions placed on Israel for observing Passover do not transfer to our observance of Communion.