Yes, Obama was born in Hawaii with an American mother and a Kenyan father, with British citizenship. He at least was born in the US. Cruz was born in Canada with an American mother and a Cuban father, with Cuban or Canadian citizenship, who knows.
Have you seen a Consular Report of Birth Abroad for Cruz? I haven’t. His Selective Service was allegedly procured through application of a Pell Grant with much of the form not shown or redacted. Did his parents just waltz back over the board or did they fill out the proper paperwork? Did his father renounce his Cuban citizenship and become a Canadian citizen or not? He did not become an American citizen until 2005.
“He did not become an American citizen until 2005.”
That should be the argument about eligibility.