There *is* a single correct parenting strategy, and anyone who says otherwise is denying that truth exists.
The right way to parent works something like this:
it can't return an answer unless you give a situation as input.
the situation includes the location, the details of the problem, a list of the people involved, etc
the people are complex data structures, including physical characteristics, their history, and their minds.
their minds are complex data structures with all their ideas.
if you change any of the people, or even change one idea in one person's mind, then you are calling how_to_parent with a different input, so you might not get the same answer.
when we say "there is one right way to parent" we mean that for one input, there is one correct output.
what does the how_to_parent function do with its input? it looks at the input and then calls a sub-module depending on what type of problem it is. it has lots of sub-modules that are specialized for different sorts of problems, and it just directs the question to the right one.
it's the same with morality. if we say "there is one moral truth" we mean for a given input situation, including every last detail, there is an answer, and it doesn't change if you ask the exact same question again, with the exact same inputs.
this explanation has a problem. people think it's so trivial and obvious that they get bored and tune out. it seems pedantic, and unnecessarily precise.
however, those same people constantly make mistakes about the exact issues i just covered.
then there is also the legitimate issue that the same situation never happens twice. so what use is it that there is one truth, one right way, if it's not re-usable? if i find a truth, and use it, why would you want to know it, since you'll never face exactly the same problem?
the answer to that has to do with the reach of knowledge. but that is advanced epistemology that people don't know about.