Clearly parent is not talking about children born in USA, so your second point is not relevant. Your first point is just a restatement of parent.

The grant-parent said "children of _illegal_ immigrants" and the parent is talking about "children of _Green card holders_". Green card holders are those who have immigrated legally.

The question of the thread is to what extent non-citizens have particular rights. Parents cite two distinct yet substantially similar groups of non-citizens (one presumes that children don't have much agency with respect to the circumstances of their immigration). Both examples argue in the same direction on the question of the thread, so why does this distinction matter?

Is the first point a constitutional issue? I don't recall the constitution guaranteeing anyone a public education.

It doesn't require public education, but it restricts discrimination if it is provided by the state, as all states do. So, yes, it is a Constitutional issue.

Which part of rhe Constitution forbids discrimination based on citizenship status?

No part of the Constitution entirely forbids discrimination on any basis, but the part that is held to limit state discrimination on that basis is—as limits state discrimination on every basis—the equal protection clause of the 14th Amendment.

The equal protection clause applies to citizenship status. The key case on citizenship discrimination and public education is Plyler v. Doe, 457 U.S. 202 (1982) available at https://www.uscourts.gov/educational-resources/educational-a...

Even foreign diplomats' kids?