LOL! I'm stunned by your witty repartee.
Just about everyone over 40 knows about serial commas.
You act like a rule for reading the English language that has been commonly used for at least a couple hundred years is some how immaterial, yet you blabber on like you are the font of all knowledge.
The first part of the sentence said who are foreigners, aliens,
The second part:
who belong to the families of ambassadors or foreign ministers accredited to the Government of the United States, but will include every other class of persons.
It does not say: who are foreigners, aliens, or who belong to the families of ambassadors or foreign ministers accredited to the Government of the United States
It would be like saying: I like my neighbors, the Amish who live near my house, who provide milk from their farm to my family at no cost.
In that sentence (yes awkwardly constructed but grammatically correct) you are not saying you like all your neighbors or all who live near your house who have a farm or even all you Amish neighbors, but only the Amish neighbors who live near your house who have a farm and who also provide you with free milk.
And you completely ignored and failed to address everything else I said. Congratulations for your witty repartee and your reading comprehension fail.