What is 1401 part of? Rules of immigration and naturalization in which the 1868 Act is a part of.
And even though Pt 1 of section 12 of Title 8 says, Nationals and citizens at birth, the key is
1401(a) a person born in the United States, AND subject to the jurisdiction thereof;
As it is for the naturalized, so it is for the one born and what does the naturalized have to do before becoming a US citizen ... renounce any & all foreign allegiance.
Per law, did Ted have to renounce a foreign citizenship that he had since birth?
This isn't rocket science, it is called natural law, the child is the nationality (tribe) of the father. God set this law in place at creation and until the last century, it was upheld by all nations.
No, Congress was not given authority over “naturalization”. Congress was given authority over the rules of naturalization which is a much larger set.
Naturalization does not and can not occur at or before birth. It only occurs after birth. That is specifically defined in Title 8 section 1101 subsection A part (23). If someone is born a citizen, they do not ever need to be naturalized. There is NO requirement for US citizens to renounce any status confired by any other nations - as the laws of other nations are irrelevant to US citizenship laws.
Further the code you pointed to, USC Title 8 Section 1481 deals only with the voluntary loss of citizenship. Note the word “voluntary” in section A:
(a) A person who is a national of the United States whether by birth or naturalization, shall lose his nationality by voluntarily performing any of the following acts with the intention of relinquishing United States nationality—
Further, I challenge you to identify any such actions taken by Sen Cruz.