To say that Christmas is for Christians and therefore excludes certain groups or individuals is to misunderstand what Christmas is. When Christ was born the angels did not declare a holiday for Christians. They declared peace and goodwill to all people. When Christ was born, Christendom did not exist. The birth of Christ was declared to Jews and Gentiles (i.e. everyone). Some were happy about it (like the shepherds and magi) while some were furious (like King Herod). Nevertheless, Christ came to all of them. There were no exclusions.
The same can be said today, for Christ maintains an open invitation for everyone. Whether Jew or Greek, bond or free, male or female, Christ excludes no one. Whether or not you believe in Christ or even God is irrelevant. Christ came for you, and the invitation remains open even if you throw it away every time it arrives. So, Christmas does not exclude people, but there are people who choose to exclude Christmas.
Imagine throwing a party and inviting everyone in the whole world. Everyone would get an invitation, but not everyone would come. Now, imagine being in school and being the only student in your class that did not get an invitation to a party. That would be exclusion. At some point in life, most of us know how it feels to be excluded from something. It can be hurtful. But that is not how Christ operates. He unceasingly invites everyone with open arms and people flee from Him. He excludes no one. They may freely choose to exclude themselves for a host of reasons. But to claim that Christmas is not for everyone is to entirely miss the point of what Christmas is.