If users have not behaved peacefully in this very same community, albeit on a different platform, then past conflicts are ABSOLUTELY your problem as a moderator. On one hand you're saying you want people to feel safe and on the other you're stating that even if a user has previously made members of your community feel unsafe, as long as they behave peacefully from this moment on you have no problem allowing them to participate in your community.
If users have not behaved peacefully in this very same community, albeit on a different platform, then past conflicts are ABSOLUTELY your problem as a moderator. On one hand you're saying you want people to feel safe and on the other you're stating that even if a user has previously made members of your community feel unsafe, as long as they behave peacefully from this moment on you have no problem allowing them to participate in your community.