AllahkaBanda

My friend you perceive the apparent contradiction due to misunderstanding and mixing up two things, let me clarify it for you to best of my knowledge:

1 - The ayah refers to not forcing people to accept Islam - hence no compulsion in religion

2 - The hadith refers to bringing justice within society by getting rid of evil, oppression, injustice and such and the hadith describes three ways to do it.

Do you see the difference between the two? The difference lies between bringing justice and making people accept Islam. The former isn't ruled out by the ayah, "no compulsion in religion". I hope this makes sense and indeed the Lord knows best!