In our society I think there's a belief that most instances where parents try to interfere with dating choices of their children it doesn't help.

An excellent point, although I think this belief is much more widespread among liberals than conservatives. And I think it's part of a larger point, which is that liberals seem to be far more negative across the board towards parental involvement in their children's lives. I vividly remember my own shock and incomprehension when I first encountered this attitude - that young people need to challenge, overturn, or break free from parental authority. I still have to remind myself that some people think like this, because it's so alien to my understanding of the world. For me it is completely natural that I would want my parents to intervene in my dating life - whether to set me up with someone they considered suitable, to warn me against someone unsuitable, to advise me that I am lacking, or whatever else - because they know me better than anyone else, and they can only have my best interests at heart. Of course I should try and adopt and carry on my parents values as best I can. And so on. I don't think it's purely a liberal/conservative thing, but I do think it's part of it.

Examples: I recently saw this article cited as an example of unfit parenting because they see their kids as "raw materials for their culture cloning project," and I saw this post heavily upvoted. My reactions were exactly opposite - my reaction was to applaud the Christians' attempts to pass down their values (although I do not personally share them) and to sigh at what seemed like the narcissism of the Lesswrong poster.

Predictions (Because any theory is worthless if it doesn't make them): I predict that conservatives would be much more willing than liberals to support statements like "Parents should make sure their sons grow up with manly skills" and "Parents should intervene when they see their children making bad choices in their romantic lives."