Hanukkah is a celebration that is established in Maccabees - books that the Jews have deemed non-canonical. I cannot understand how a Jew could simultaneously believe Hanukkah is a mandatory feast, while rejecting the very book it is established in as being not from God and only a historical record. If the book is not from God, the feast is not from Him either.
But there's absolutely nothing wrong with celebrating it. It's a commemoration of a historical miracle. Any excuse for a party is good!
We do know Jesus happened to be in Jerusalem once during Hanukkah (John 10:22) - but we have no idea whether he travelled there specifically for the feast, or if it was a coincidence that he was there at the time. We don't know what He thought about it. He also hang out with prostitutes - but we obviously don't read that and assume that he approved of prostitution and made a habit of obtaining their services. The only reason anyone would read that he was at the temple during Hanukkah and assume that meant he was approving of and promoting that feast would be if someone already believed that feast should be celebrated, and was looking for a proof-text to justify their predetermined viewpoint.
But even if he didn't promote it, there's nothing wrong with commemorating it.
Easter is a commemoration of a historical miracle also - a far greater miracle. The date modern Christians commemorate Christ's death and resurrection is obviously usually different to the date modern Jews celebrate Passover - but that is solely because Christians and Jews use different calendars to calculate the date. There are multiple Jewish calendars (different Messianic groups celebrate Passover on different days), and multiple Christian calendars (the established Catholic and Orthodox ones, and various historical ones that are no longer in use). But all of these calendars attempt to calculate the date of passover (to greater or lesser accuracy). All the changes to calendars over time (and yes the standard Jewish calendar has been changed too) are aimed at attempting to get more accurate dates.
As far as I can see, we should remember both Passover (as a mandated feast day) and the resurrection of Jesus (as a foundational event crucial to our faith). How and when we do that is something we could debate forever, but that debate would only be about a lesser detail (precisely when to do it, which calendar was best etc). The important thing is that we remember both.
But eggs and bunnies are obvious pagan symbolism that has nothing to do with Christ. Eggs in particular have infiltrated both Easter and passover - the standard Jewish passover seder plate also includes an egg. The Jews have all sorts of religious-sounding justifications for this, and Christians have a different set of justifications. But as far as I can see this indicates pagan contamination of both celebrations, from an identical pagan source.
I personally believe passover should be celebrated with a simple meal, modelled after one or both of the simple meal specified in Exodus, and the last supper Jesus had with his disciples. And the event should be used to commemorate both the Passover and the resurrection. This avoids the pagan contamination inherent in the seder and chocolate bunnies.
But the date is not worth debating. We're just talking about finding a time when the earth is in a similar relative position to the sun and/or the moon to what it was at a date in the past. Really, dates are nothing but physical positions. They are meaningless. The actual event happened in the past, and the past cannot be repeated. Calendars help to remind us to remember something at somewhat regular intervals, but they really don't matter much. The remembrance itself is what matters.
The birth of Jesus is also a foundational event crucial to our faith. Whether it should be celebrated on a particular date is up for debate, but I don't see any sin in doing so.
However in remembering his birth, like remembering his death, it is important to reject paganism. We do not attend pagan Yule celebrations (there is a community Yule celebration every year in our local area, which we intentionally do not attend). We do not even have a Christmas tree in our house. We must not allow our godly celebrations to be contaminated with pagan practices.
