... would it be morally right for the US government to take a closer look at all immigrants who are exactly 5' 6'' tall?

No.

It might be okay to discount all people who weren't 5'6" tall, but that doesn't even make sense. (For example, Hitler wanted to get rid of all Jews and all people who weren't blond-haired and blue-eyed, despite the fact that he was quite swarthy and ethnically Jewish.)

It is never okay to assume something about someone based on factors that person cannot control.