I think you meant non-secular holidays, but anyway.
Christmas in the US was restarted in the mid-1800's as a family holiday, not a religious one, and it's true origins go back thousands of years prior to the rise of the christian religion. My family has never been religious and we have never treated this as a religious holiday, but a day for spending with family and friends, and spoiling kids rotten.
Easter is also another holiday that predates the christian belief system, and in fact still remains named after a pagan goddess Oestra although it has had many different names in different cultures. Easter was more a rite of spring than anything else, and we treat this also as a day for spending with family and friends and giving our children more candy than they should eat. Oh also, it is the only time of year that I will actually eat ham.
Holidays, no matter who claims them as their own, are just days and the meaning one puts into it is what matters.