Purim customs are Jewish customs
Instead of looking at the sources, the people who advance this fallacious position rely on the post hoc ergo propter logical fallacy. As Easter is always tied to Pesach in the calendar, the day before Ash Wednesday always come out a week or two before Purim. Ah, if it follows, we, too must be following. The Jews of Italy saw the nonJews having a rollicking good time before the sober time of Lent and decided that they, too, would like to party with a masquerade. And they tacked that on to the holiday of Purim. So that theory goes. It simply ignores two points -- halacha and history.
In http://www.yeshiva.org.il/ask/eng/default.aspx?cat=15&page=2&rc=328, Rabb Moshe Leib Halberstadt cites various references to the custom in halachic contexts:
The earliest sources I found to the costumes custom in various events is from the era of the Rishonim in the 12th century. In Sefer Yereim of Rabbi Eliezer of Mitz, one of the Baalei Hatosfot and the disciple of Rabbeinu Tam. Also in a responsa of the Rambam quoted in Sefer Maaseh Rokech of Rabbi Masud Chai Rokeach.
The earliest source I found that refers explicitly to Purim costumes is from the end of the era of the Rishonim, in the Musar Sefer Even Bochen of Rabbi Klonimus B"r Klonimus of the 13th century.
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