Without actual numbers and rational arguments, this is so subjective it is moot.
People arguing against this aren't against fighting child sexual abuse or even sexual abuse in general. But the entire thing is so riddled with "what ifs" and more, that it's a hard sell to justify another step to the road of potential total control.
Every parent wants their children to have as many lifelines as possible in case something bad happens, to let them experiment safely without predators lurking. What we should be asking is how much we're willing to give up for each lifeline, and at what point we have to accept nature (or in this case, society) just isn't going to be fair.
"In recent months, Johansson has stressed that privacy and encryption should not stand in the way of law enforcement"
my values, on the other hand, are the exact opposite (law enforcement should not stand in the way of privacy and encryption), and thus dictate a different preference.
Not every value is as other value.
From your description he seems very irrational and led by emotion. His goal is noble but that's where it ends. The road to hell is paved with good intentions.
Once the emotional tearjerker arguments have been used to support those things, the cynical bureaucrats and autocrats that make policy later use these tools for so many other sinister things. If Kutcher has more brains than emotion, and is serious about a genuinely better world, he should be aware of these other important fundamentals too and base his proposals for fighting exploitation on them.