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.
If a kid doesn’t like one of their parents because they are forced to do chores and eat their veggies, should the kid have a say in whether or not that parent gets to stick around? I’d argue no, because as a child, the mind is not fully developed and decisions are coming from a possibly hormonal, emotional child. It would be foolish of a parent to ignore a child saying they don’t like someone if the reasoning makes sense, but kids dont get to decide the lives of their parents. If a new person is coming into the house and makes the kid feel uncomfortable for legit reasons, not, “I don’t like them”, then their opinion matters. Outside of that it carries very little weight, because kids are fucking stupid.