Thank goodness this never happened to me cause my parents were good parents, it’s just as much the childrens home as the parents and children should be allowed to say “I don’t feel comfortable with another man or woman living hear” Its the parents responsibility to make sure their children are comfortable and feel safe around a new adult. The parent should plan a public meet and greet parent, child, step and after each one the children should have the right to say no more and it end there.
Good parents take care of their children, and provide a safe home to live in; however the children do not have an ultimate say. A good parent would have a discussion to explain the situation and also be sure the person moving in is safe to have around the children they’re responsible for, but ultimately the grownups pay the bills, put clothes on the children’s backs, and put food on the table. If the child feels entitled to an equal share vote in the household decisions then expectations should be managed.