The yeast in Galatians was the false brethren, those of the group of the circumcision who introduced false doctrine. And Jesus also makes reference to yeast being false doctrine in Matt 16:11,12. Thus yeast refers to both sinful behavior and false teachings.
In contrast to these, the unleavened bread is that of sincerity and truth. Jesus represents this unleavened bread. For the communion service in which Jesus associated his flesh with the bread, was actually a celebration of the week of unleavened bread just before the Passover. Yet how sincere are Christians today? How concerned about truth? Christians should not be involved in lying, slandering and falsifying information. They should not put on a false face or speak deceitfully.
It doesn't take much hypocrisy to corrupt the whole church.