Why Do Some New Testament Passages about Salvation Ignore Faith and Focus on Works?

Questions about why some passages about salvation in the New Testament (e.g., Matthew 25:31–46) seem to focus on works rather than trust in Jesus and whether the symmetry between Adam and Jesus described in Romans 5 indicates everyone will be saved from Hell.

• Why are there so many passages in the New Testament that seem to focus on works rather than trust in Jesus when it comes to dividing the saved from the unsaved?
• Doesn’t Matthew 25:31–46 sound like we’ll be saved by our deeds rather than grace?
• Since Romans 5:18–19 talks about the symmetry between being condemned in Adam and righteous in Jesus, would that mean that just as we don’t opt into Adam’s sin, so we don’t opt into Jesus’ salvation, and therefore everyone will be saved from Hell?