It's a really complex issue; ultimately it is a complex issue between two adults, and doesn't necessarily mean that the abusive parent is going to be abusive to their children. On one hand I question why should children lose out on a relationship with a parent who is never going to cause any direct harm to them? On the other hand, I wonder if we need to do more to protect children from being involved with people who display abusive behaviours towards others, not only to protect the children, but also to ensure abusive generational cycles are broken.
Abuse occurs within a spectrum; what you see as abuse may not be what someone else sees as abuse. What you see as abuse, may also not be what the courts view as abuse. I am not saying this to minimise any type of abuse, it is just a very difficult matter to deal with. Should a parent have no contact with their children if they haven't been found guilty by a court? What happens when someone makes a false allegation of abuse i.e. why should that also impact the children?
Different cultures and different religions have different expectations and standards; in some cases outsiders view these customs as abusive, or oppressive, yet to the people who hold these values, these are inherited cultural values - who decides then what is the line of abuse that needs to be crossed to stop children having access to a parent?
There are cases where men are not allowed to have further contact with their child(ren), so yes, it does happen that in some cases all contact is stopped as a way to safeguard the child. However, if there is no safeguarding issue between the parent and the children, then I am not really sure stopping all contact is actually the most appropriate course of action for the development of that child. Relationships that are severed in childhood are often impossible to reinstate when the child is over the age of 18 (i.e. when it would be the child's choice). If there is no risk to the child, why should contact be severed and the child suffer the huge, and very detrimental, loss of "losing" a parent. This is not a decision that should be taken lightly; attachment, and specifically broken attachment patterns, can lead to disastrous consequences for a child. Research has demonstrated that these consequences can, and often do, last throughout a chid's adult lifetime.
It is my belief children should not be punished for the actions of a parent, so, unless there is a risk of harm to the child, contact with parents who have been accused of abuse should always be maintained.
If there is any risk to the child, or abuse directed towards the child, contact should be stopped.