Good point.
I maintain that there are very few Americans who would hold against Cruz, whether they would ever vote for him or not, the fact that he was born to an American citizen mother, left Canada at age THREE and has lived continuously in the U.S. for the last 42 years.
There have been surveys on that. I think somewhere around 25-35% of the people who are asked if a person born in Canada to US parents is eligible, say no. They might vote for him anyway, since eligibility is not required to hold the office.
I don't know if that comports with your sense of "very few." Just saying, I'm not disagreeing with you. I'd vote for a naturalized citizen for the office, myself, if they were strong on the borders and strong on personal independence, RKBA, etc. I might even vote for a foreigner for the office, Netanyahu would be great, Thatcher was awesome.