Luxor does not close anything for Christmas Day, 25th December, in fact as the locals are a mixture of Muslim and Coptic Christians there is no local that celebrates anything on that day. Coptic Christians follow the old calender (also known as the Julian or Coptic calender) and celebrate Christmas 13 days later than the West which uses the Gregorian calender. Muslims whilst they revere Jesus as a prophet do not celebrate his birthday, in fact birthday celebrations are not common full stop. So there is nothing happening on Christmas Eve or Christmas Day except at tourist establishments. Hotels and restaurants seeing the demand have started offering gala dinners to their guests and decorating the buildings but do not expect anything more than that.
New Year is likewise, it is not a local holiday as the Muslim and Coptic new years fall on different dates and even then there is no tradition of celebrations. So only expect celebrations in tourist establishments.
There is no effect on site openings, indeed the sites never shut not even for Eid, the only event that does effect the sites is closing times during Ramadan. Opening times remain the same.