Yes, it is appropriate to use the greeting Happy Holidays rather than Merry Christmas. Merry Christmas, as a greeting, refers to only one holiday. Happy Holidays is used to encompass all holidays during the Holiday season, including the Christian holidays, Three Kings Day and Christmas, the Jewish holiday Hanukkah, and the secular holiday, New Years. In fact, it is not only perfectly acceptable use both greetings interchangeably, they can also be used in conjunction with one another to wish someone a Merry Christmas and Happy Holidays.
The primary holiday season in the United States, and many other countries, runs from November into January and includes a number of celebrations. Consequently, practical reasons exist to extend the greeting of :happy holidays during this time period rather than merry Christmas. In addition, by using the happy holidays greetings, a person is able to avoid the possibility of using an inappropriate greeting to a person who may not celebrate a specific holiday.
Happy Holidays is an appropriate at large greeting because not everyone celebrates Christmas. Kwanzaa, Chanukah and the Winter Soltice are just a few of the other holidays celebrated around the same time as Christmas. Furthermore, some people celebrate nothing at all during the holiday season. It is, therefore, more inclusive to greet people, particularly those you do not know, with Happy Holidays rather than Merry Christmas.
While Happy Holidays is not offensive in and of itself, the impetus behind its creation and promotion is a negative reaction to Christian tradition. Christmas exists to celebrate the birth of Christ, as much as secular society would like that not to be true. Saying Happy Holidays instead of Merry Christmas is a feeble attempt to change the reason for the celebration.