With respect to Ted Cruz, when did they change the constitution to allow foreign born people to become president of the United States?
The Constitution does not prohibit "foreign born people" from becoming president of the United States. The Constitution requires that the president be a "natural born citizen". Cruz is not a naturalized citizen. He has always been a citizen of the United States. The question is whether that qualifies as "natural born".
If Cruz were to be nominated for the Republican ticket, I doubt very much that anyone would challenge his eligibility in courts who would have to rule on the issue. But even if someone did challenge his candidacy, I doubt very much that the supreme court will be willing to even accept the challenge.