Ageism is a legally defined form of discrimination as well as the subject of ethical discussions. It's a real, defined thing. Just because we disagree on what qualifies as ageism doesn't mean you get to call foul and say it's irrational/emotional.

This is literally a “think of the children[‘s freedom]” appeal. You’re not arguing for or against the restriction on its merits.

In the US at least there’s also no such thing legally as age discrimination against minors so far as I’m aware.

Edit:

Let me frame this differently. “Ageism” is basically by definition bad, so applying the term “ageism” to a restriction is a an attempt to label the restriction bad without establishing that on its own merits.

If you try to provide a consistent definition of “ageism” that applies to restricting access to the internet but not restricting access to alcohol, you will most certainly have to resort to phrases like “reasonable restrictions” (if not, I’m very interested in your definition), which means that there’s still a need to establish what is reasonable. Applying the label “ageism” without establishing reasonableness is then a circular argument.