May a Catholic Celebrate Muslim Holidays?

I assume you are referring to the two Muslim holidays, Eid al-Adha and Eid al-Fitr. Whether or not a Catholic should participate in these festivities depends on the circumstances. A Catholic could attend a private holiday celebration as a guest of Muslim friends or could participate in interreligious activities sponsored by a Catholic diocese in conjunction with local Muslim communities. However, there would be no reason whatsoever for a Catholic to celebrate these holidays as part of a personal religious observance, since these holidays are not part of the Catholic religious tradition.