Summary: You can destroy someone's hearthfire when one of the following conditions has been met:
- You have vandalism and have criminal act enabled. Be warned that attempting to destroy it will cause you to leave a vandalism scent.
- The hearthfire is within your own personal claim (village claim won't work without vandalism).
Since hearthfires have a soak value of 5, you need to deal at least 6 damage to be able to destroy it at all. This means you need 36 strength barehand, 25 strength with a stone axe, or 16 strength with a pick axe. Also hearthfire have a good amount of structural HP so having waterskin/flask and a bucket of water is highly recommended.