The first Christians were Jewish. In fact, Christianity is really "fulfilled" Judaism, in that the fulfillment of the Messianic prophecies are found in Jesus. So, Jewish Christians (or Messianic Jews) celebrate Jewish holidays today and always have--even from the time of Christ.
There is no prohibition to non-Jewish believers regarding the celebration of other holidays, and Christianity is not about prohibitions anyway, but about forgiveness and redemption through faith in Jesus. It is true that we are called to holy living, so as long as the celebration of holidays does not impede holiness, there really isn't any problem with that.
Of course, the celebration of other deities would be prohibited whether or not it is done on a holiday or not.
This could be considered an area where it depends on individual conscience, like eating meat sacrificed to idols that Paul mentions.
As a footnote, Christmas and Easter can be celebrated in completely secular ways, which I would say is not wrong, but definitely not Christian. If Christmas is focused on getting gifts and a fat man in a red suit, there's really nothing Christian about that. And rabbits and eggs certainly do not qualify for a celebration of the single most important event in all Christendom. So, even celebrating religious holidays does not mean that those are sacred observances, if they are done in a secular manner.