Before Alma the Elder receives the revelation about how to regulate the church with appropriate discipline measures, there is a period when the unbelievers gain a lot of influence.
For it came to pass that they [the unbelievers] did deceive many with their flattering words, who were in the church, and did cause them to commit many sins; therefore it became expedient that those who committed sin, that were in the church, should be admonished by the church. (Mosiah 26:6)
But once Alma the Elder receives his revelation about how to deal with those who sin and is able to reaffirm the principle that eternal salvation depends upon continued repentance and faith in Christ, those people who were willing to repent changed and became steadfast and immovable, willing to keep the commandments, unwilling to listen to those who previously had deceived them.
Of course, the unbelievers did not like to lose their influence, so they ratcheted up the pressure to the level of persecution, which is why v38 tells us Alma and his fellow laborers were “persecuted by all those who did not belong to the church of God.” Unbelievers think church discipline is unfair and unmerited, but the church lives at a higher level.
The members were also persecuted, since Mosiah 27:1 notes that “the persecutions which were inflicted on the church by the unbelievers became so great that the church began to murmur and complain to their leaders concerning the matter.”
Persecution over church discipline measures is an attempt to influence with social aggression and shaming and mockery. It is also an attempt to reject and punish. However, for those who are willing to accept church discipline, the blessings are becoming steadfast and immovable in Christ.