"Conscientious parents" refers to mothers and fathers who take their responsibilities seriously, put in effort, and are careful in their decisions and actions when it comes to raising their children. Full definition
I know a lot of kind, thoughtful people who don't have strong bonds with siblings or cousins, and good, conscientious parents whose kids don't particularly like each other. (thehappiesthome.com)
It is surely good for babies to have conscientious parents who want the best for their children. (articles.chicagotribune.com)
I don't believe that it is wise for parents to follow any recommendations blindly, and I don't imagine that even the most conscientious parents do. (amotherinisrael.com)