Psalm 145:20a continues the thought of the preceding text, but in Psalm 145:20b the downside is discussed: he will destroy all the wicked/ungodly. Note that this is not said specifically of those who suppress the believers but of all the ungodly.
We see the following line to the New Testament:
Enemies are met with love (think of the teaching of Jesus) and they are offered peace (Ephesians 2:17).
Those who reject God, however, will be destroyed (as Psalm 146:1–10 says). Unlike what the Old Testament reflects, this will not happen in but after this life.
20 The LORD preserves all who love him, but all the wicked he will destroy.