Translation:The noses of the men that sing are red.
The use of "that" to refer to people is less common, but not incorrect.
"The notion that that should not be used to refer to persons is without foundation; such use is entirely standard."
But I grant you that it's used more after pronouns like "anyone" and "someone", than after nouns. And that it would make more sense to use the more common "who" here.