Only if they are not citizens by birth.
Their acts have naturalized Cruz.
Not so. Ted Cruz is a citizen by birth. He was never naturalized because he didn't have to be. If he were naturalized, he'd have a naturalization certificate. You produce one of those in Ted Cruz's name and I'll switch sides in this argument.
He needed the power of congress to write law for his citizenship to be.
What gives you this idea? And even if true that legislation extended natural born citizenship to those born outside the US, that is merely an expression of what natural born citizenship already is: the recognition of the natural affinity of a child for the societal and family ties that bind the child to the parent's homeland and polity.
Think for a moment about what you are proposing and the unintended consequences. My God!
I see you wrote parent's and not parents'.
What of the societal and family ties of a person born to citizens of two different nations?
From the Constitution: No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President;
At the time of the Founding there were NO natural born citizens of the U.S. Everyone who was a citizen of the U.S. at the adoption was born to two parents who had not been citizens of the U.S.
The Founders explicitly excluded such people from the prohibition but included a prohibition which would eventually restrict eligibility such that some citizens would not qualify.
I can imagine no reason for excluding such persons aside from the possibility that their loyalty might be in question. Despite any concerns over what was "fair" some citizens were to be excluded from the Presidency.
What possible sense would it make to exclude only those who had two foreign parents. How is a person's loyalty not divided by having even one parent who is not a citizen?
The Founders would have envisioned a nation teeming with "natural born citizens" and would have had no qualms whatever about excluding those with a lesser tendency to disloyalty than those we all agree were to be excluded.