“It’s difficult,” Dr. Ibrahim said, noting that he would not be here if that kind of policy had been in place when his father wanted to leave Cairo. “I just have to believe that those people have not met the right individual. There are a lot of people who never meet Muslims who are kind, gentle and giving.”

Stephen Miller, a policy adviser to Donald J. Trump, said Mr. Trump — who has spent months condemning immigrants from Mexico and the Muslim world — simply wants to “select immigrants who support, defend and uphold our values.”

Mr. Miller described Mr. Trump’s proposal to stop all immigration from Muslim countries until a broad security assessment could be put in place as “about as mainstream and common sense as it gets.”

But Dr. Ibrahim said what he heard was mostly an appeal to ignorance and fear. He said he moved to Orlando from Tennessee in part so his twin boys, who are 11, could grow up around different kinds of people. Like their father, whose looks make him hard to place in terms of ethnicity, they represent a mixture of cultures: Their mother is white, Anglo in the lexicon of Orlando, born and raised in Tennessee.

But as a family with Ibrahim for a last name, they are still sometimes seen as outsiders. Dr. Ibrahim said his wife was once denied a loan because her name was confused with someone on a European terror watch list.

He and his wife also struggled with whether to continue the tradition, common in the Middle East, of passing on his second name, Abdellatif, to their oldest son. In the end, they went for it: Abdellatif now links grandfather, father and son, three generations of Egyptian-Americans.

Dr. Ibrahim is hoping that he won’t regret it. “Hopefully by the time he’s of age,” he said, “people will be even more tolerant.”