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Abbreviated version:
"I thought that that wasn't a thing in the U.S.A. anymore at all!"
Entire sentence:
"My entire world was blown away when I heard that 800,000 kids in America (the U.S.A.) work illegally, because I thought that that wasn't a thing in the U.S.A. anymore at all!"
Grammatically it is correct. The first 'that' would be a conjunction; something like 'I thought that' or 'I feel that'.
The second 'that' would be a pronoun, such as 'that wasn't a thing' or 'that was no longer acceptable'.
Structured together would be:
I thought that that wasn't a thing anymore
I thought that that was no longer acceptable.
If it bothers you, you can usually remove one of the "that's", leaving you with: "because I thought that wasn't a thing in the U.S.A anymore".
Hope this helps!
