Is it okay to answer that anon through your inbox? When I converted, I decided to still say "Merry Christmas", give gifts, and attend gatherings for the holiday even though I'm Jewish. Why? Well, instead of having a battle over my identity and viewing it as "my own tradition", I view it as "these are people I love of a different religion, and I want to celebrate with them". A Christian can be invited to Passover dinner, so what's wrong with being invited to a Christmas party?
This is one possible (liberal) approach to this sort of question! However, you will find that in circles with stricter interpretation of halakha, this is a problem.
There’s no problem with inviting gentiles to a pesach seder, but we (as Jewish people) are told to avoid hukkat ha-goy – meaning avoiding gentile practices (especially those that are religious.) This is something that is often balanced against the concept of mipnei darkhei shalom, or roughly doing something “because of the path towards peace.”
On the one hand, many Jewish people do not feel comfortable attending Christmas parties or saying Merry Christmas, because this is a gentile practice and we’re commanded to not do those things (especially ones related to another religion). On the other hand, a convert whose family celebrates Christmas may feel that for the purpose of peace (and not drawing negative opinions towards Judaism) that participating in familial Christmas events is acceptable. These things are often navigated in interfaith families (and converts are often included there!). There’s an interfaith family website that might have more suggestions.
I think I personally my balance is this: I don’t mind giving gifts, and I won’t refuse to be in my Nana’s home because she’ll have a Christmas tree up. (My uncle is flying me home for my other grandmother’s memorial service next week.) But I am well past any kind of Christmas mass attending. If Las Posadas happens, and the procession comes to their door, I will watch it and admire it as an outsider, not as a participant. If that makes sense? I definitely fall on a liberal side of things.