Any writing carries within itself the spirit of its writer.
In the Psalms of David, we find the Spirit that guided him: The Spirit of God Almighty.
Because of this, anyone, regardless of their religion, can always find a word to meet their needs in Psalms.
The God of Abraham continues speaking to those who have ears to listen to His Voice. However, what is most important when reading Psalms is not feeling comforted by their messages, but to follow, practice, observe; this is, obey what is being taught.
Otherwise, that sense of comfort will pass and despair will strike again.
Don’t waste your time comparing your life with the life of evildoers who prosper, nor envy their achievements. Instead, take care of your own life.
Concern yourself with obeying the teachings of the Spirit of God and He will answer by taking care of your needs.
Put His teachings immediately into practice, just as a seed is placed in the earth. Surely, it will sprout and bear its fruit.
DO NOT fret because of evildoers, nor be envious of the workers of iniquity.
For they shall soon be cut down like the grass, and wither as the green herb.
Trust in the Lord, and do good; dwell in the land, and feed on His faithfulness.
Delight yourself also in the Lord, and He shall give you the desires of your heart. Commit your way to the Lord, trust also in Him, and He shall bring it to pass.
He shall bring forth your righteousness as the light, and your justice as the noonday. Psalms 37:1-6