The Latin rite of the Catholic Church does not require abstention from meat on Christmas Eve. I do not know if the Eastern rites do require it, but you can post the question in the Eastern Christianity forum for an answer.
St. Francis of Assisi was once asked by a brother friar if Christians should abstain from meat if Christmas fell on Friday. To the contrary, St. Francis is said to have replied, even the very walls should smeared with meat on such a day so that they too could share in the joy of the holiday.
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