It all depemds on how it is used in the context. I think "the" is ok. On the Mid Autumn Festival Day, it a Chinese tradition for families to celebrate with everyone in the family.
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OntheMid Autumn Festival Day, it a Chinese tradition for families to celebrate with everyone in the family.
At the Mid Autumn Festival celebration, everyone had a cheerful time
There is nothing wrong with your second sentence, since 'the' refers to the common noun, 'celebration'. It is your first sentence that should omit the article, just as we omit it for