Is a person who has been convicted of a barrier crime allowed around children?

No, convicted sex offenders are not. If the person has been arrested and eventually released from prison; the judge will give orders that they are not to live or be within so many blocks of a children's play area, school grounds, etc.

We frequently hear news stories entailing parents who are irate when a sex offender is living in their neighborhood. How can you blame them? It is the responsibility of all of us to protect children. It does not matter if the children are yours, or somebody else's.