As the Wikipedia article demonstrates, 'think of the children' is not usually a motivating factor, it is a way of stymieing criticism by implying the opponent is sociopathic and doesn't care about children. It is similar to accusing someone of racism or sexism, in an effort to shut them down. These tactics are all very effective in our currently sociopolitical climate.
Unfortunately, it is almost impossible to use this tactic to advocate in favor of something (rather than against it).
I wish I had a suggestion for how to parry the accusation, but I don't.
I think we have to go on the offensive. We can use Think of the Children to promote legislation that mandates strong encryption on online platforms. It can also prohibit any legislation that tries to incentivize companies to weaken encryption, like the EARN IT act. Maybe the latter will require a constitutional amendment, I'm not sure.
Without a law like this, we're just going to keep fighting the same battle every 4-6 years. They only have to win once, we have to win every time. It's not a fair fight.
I strongly favor end-to-end encryption, but I just don't see 'think of the children' working as an effective message in favor of anything.
I happen to believe that it was protected by the first, fourth, and ninth amendments, but I am not sure it is possible to erect permanent legal bulwarks against ever-expanding federal powers. As an example, the second amendment specifically enumerates gun rights, yet it is under constant assault. The only way I can see to protect this type of individual liberty would be to radically de-scope the federal government, but I don't think that's going to happen.
Again, I really wish I could be more optimistic, but I just don't see any realistic hope.
Unfortunately, it is almost impossible to use this tactic to advocate in favor of something (rather than against it).
I wish I had a suggestion for how to parry the accusation, but I don't.