Non-Jews are certainly welcome to celebrate Hannukah with Jews. However, it is problematic if non-Jews celebrate and adopt Hannukah by themselves, and it is especially problematic if this adoption entails imparting Hannukah with new meaning, especially new meaning that is connected with Christian beliefs or other non-Jewish beliefs. Keep in mind that Hannukah not only celebrates our survival through a near miraculous military victory over the far larger Greek Seleucid Empire as well as the rededication of the Temple subsequent to the victory, but it also celebrates successful rejecting of forced assimilation; an important part of the Hannukah story and why it was so important that the Maccabees defeat the Seleucid Empire was for their attempt to deny Jews the right to practice Judaism as well as their attempt to forcibly assimilate Jews. In adopting Hannukah, one is — in effect — being assimilationist and culturally erasing in ways that can be perceived as subverting the underlying ideas of the holiday. It's certainly possible to celebrate with each other, but please do not cross over the line into ownership.
Related answers:
- My answer to Do you think Islam and/or Christianity are culturally appropriating Judaism? Or is it cultural appreciation? Or neither? Why?
- My answer to What do practicing Jews think of Christians who observe Jewish religious holidays?
- My answer to What is the Menorah and what does it symbolize?
- My answer to If I wear a Star of David, not being Jewish, would Jewish people be offended?
- My answer to Why is calling a Jewish person a Jew an insult?
- My answer to I was born to a Jewish mother and I'm not religious. When I do have kids I would like to celebrate the holidays with them to keep my culture alive, but is it offensive to celebrate these holidays without a religious intention?