With such a peculiar title, I wondered about the biblical background and context for this song. Looking it up in a concordance, I found that the text is from Jeremiah 12:9. In the context of verses 7-10, God's people are described by many figures of speech (the comparisons used in this passage include "my house, an inheritance, my beloved, a lion, a speckled bird of prey, my vineyard, and my field").
In focusing on the metaphor of the speckled bird, we observe in nature how birds will attack other birds of unfamiliar or unusual plumage. In a similar way, foreign nations felt threatened and often attacked God's people because they were different. Throughout the ages, God's faithful people have received and will continue to receive persecution from the wicked (Matthew 5:10-12; 10:22; John 15:18-21; 2 Timothy 3:12; 1 Peter 4:16).
According to the second verse of the song, there are those who would seek to change what the church teaches. We must continue our adherence to God's truth (1 Peter 4:11; Colossians 3:17). The church is to be "the pillar and support of the truth" (1 Timothy 3:15). To avoid God's condemnation we must not go beyond that which is written, nor teach a perverted gospel (1 Corinthians 4:6; Galatians 1:6-10).
Reflecting on the last verse of the song, the Lord will one day return in the clouds and His voice will be heard (Acts1:11). Everyone needs to be prepared by being numbered among God's people (the church) for the coming judgment day.
And despite whatever persecution the speckled bird (the church) may receive from others in this life, it is small in comparison to the joys of heaven (Romans 8:18; 2 Corinthians 4:17).