Simply put, broken families and divorce rates are unhealthy. Open sexuality is viewed by many as a moral contagion that breaks apart society. Children from single parent homes are far more likely to encounter serious problems throughout life.
I'm not entirely sure where the connection between open sexuality and broken families, divorce rates and single parents is coming from.
Open sexuality, doesn't necessitate any of those things. All it means is that sexuality isn't hidden away. I.e. More education about sex (Including safe sex), more understanding of sexualities and more understanding of body diversity.
Broken families comes from individuals not respecting their partners.
Divorce rates comes from people being pushed into marriage (Which can be exacerbated by "No pre-marital sex" ideals)
Single parents comes from either unsafe sex (Made worse by the lack of education and availability of safe sex) or aforementioned premature marriages and subsequent divorces (As well as widowing which is a result of many factors such as disease, crime or war).
Nothing about open sexuality has quantifiable negative impacts, unless you have the myopic view that open sexuality = extra marital sex.
