גמרא ביצה ו'.:א'
אמר רבא מת ביום טוב ראשון יתעסקו בו עממים מת ביו"ט שני יתעסקו בו ישראל .....
Rava said: If one died on the first day of a Festival, gentiles should attend to his burial. If he died on the second day of a Festival, Jews should attend to his burial.
אמר רבינא והאידנא דאיכא חברי חיישינן.
Ravina said: And nowadays, when there are Chavarei, this practice must be adjusted. The Chavarei were Persian priests who made false accusations against Jews in Babylonia. They cited the fact that Jews were burying their dead on the second Festival day as proof that the day was not holy, and they forced them to work on that day. Since we are concerned about this possibility, we do not bury the dead on the second day.
Why can't they just explain that according to Jewish law it is permitted to bury the dead on the 2nd day of Yom Tov??
A beautiful original explanation of the Gemara here. See also תהלה לדוד או"ח סי' י"ח for פלאי פלאות.