Is it permissible for children to cut off physical contact with parents and suffice with telephone contact when there are psychological, family, and religious problems with the parents, out of fear for their faith, marriage, and households?

The rights of parents are great and do not fall, even if they are disbelievers. If their visit to your home causes harm to you and your children, you are not obligated to host them. However, you must maintain ties with them and show affection in a way that does not harm you. Filial piety includes delivering every possible good and repelling every possible evil. Among the greatest acts of piety are advising them gently, enjoining them to good, forbidding them from evil, and supplicating for their guidance.