1 Peter 3:13 makes the simple point that no one usually attacks people for doing good things. As he stated in 2:13-14, people generally do not suffer insults and persecution for doing good things (although there are always exceptions). It is better to suffer for doing good even if it is unjust, than suffer justly for doing wrong things.
The verb “zealous” may have been chosen because at this point in Judea the Zealots were beginning to coalesce into an armed resistance against Rome. Even if the “zealous Jews” were rebellion against Rome in Judea, Peter tells his readers to channel their zeal into a quiet life that is worthy of respect.
But Peter knows that “strangers and aliens” are not always fairly treated, and it is likely that they will be attacked unjustly (v. 14-15a). The syntax of verse 14 is very difficult, the ESV’s “even if you are persecuted” expresses the optative verb well. It is not that the readers are already facing regular persecution, but the sorts of slander that outsiders usually face when they live in another culture. The verb is a present active optative from πάσχω, the verb Jesus used to describe his suffering in Luke 22:15, for example, but it also appears frequently for Christian suffering (1 Peter 2:21, Phil 1:29). Peter may allude to the teaching of Jesus when he says that the believer will be blessed when people persecute them. In Matthew 5:10 Jesus says much the same thing (in the form of a beatitude).
The one that suffers for Christ’s sake has no reason for fear or trouble, probably an allusion to Isa 8:12-13. This is a significant because the original line in Isaiah referred to a time in Judah’s history when Jerusalem was threatened by the politics of the larger world. Isaiah is warned in 8:11 not to walk in the ways of the people of Jerusalem, who are afraid of the nations that threaten the city. In contrast, Isaiah is to not fear the things that the people fear, but rather to honor and fear the Lord alone.
The readers are living as strangers and aliens, among people that suspect them and will eventually begin to hate them and physically persecute them. The quote functions as an encouragement for the readers to fear what really needs to be feared, the Lord and him alone. Fearing persecution is not necessary since the Romans cannot really harm the believers (Matt 10:28). Peter has just said this specifically to the wives in 3:6, now he repeats the command to the whole congregation.