Short answer
No. Hanukkah, Passover, Yom Kippur and other Jewish holidays are religious festivals of another faith, so Muslims do not celebrate them, in the Hanafi school or the other three. Muslims do honour Moses deeply: the Prophet ﷺ fasted Ashura in thanks for Moses' rescue from Pharaoh, and told Muslims to add a day so their fast would be distinct.
Joining the religious rites of Jewish festivals, such as the Seder or lighting the Hanukkah menorah, is not permissible. Kindness to Jewish neighbours, accepting their gifts and eating their permissible food is allowed. Fasting Ashura together with the 9th or 11th of Muharram is the sunnah way of honouring Moses' deliverance.
The four schools agree on this.
Explanation
When the Prophet ﷺ came to Madinah he found the Jews fasting on the 10th of Muharram, the day Allah saved Moses and the Children of Israel from Pharaoh. He said "I am closer to Moses than you", fasted it and told Muslims to fast it. Later he said that if he lived to the next year he would fast the 9th as well, so that the Muslim fast would be distinct. Muslims honour Moses, but in their own way and on their own terms. See Ashura.
The festivals of another faith are part of its worship. The Prophet ﷺ said every people has its festival and the Eids are ours, which is why the four schools agree Muslims do not take part in other religions' festivals.
- Passover Seder: the meal is a religious ritual with blessings and wine. Politely decline to take part.
- Hanukkah at work or school: halal snacks are fine. Do not light the menorah or join its blessings.
- Greetings: avoid congratulating people on a religious festival. A warm general wish for their family is fine.
- Food and gifts: accepting a gift is fine. On kosher meat, see meat slaughtered by Jews and Christians.
Jews are People of the Book, and the Quran tells Muslims to discuss with them only in the best way. Good neighbourliness with Jewish colleagues and friends is part of Islam. See who are the People of the Book? and Moses in the Quran.
The evidence
Quran, Surah Al-Ankaboot 29:46
۞ وَلَا تُجَٰدِلُوٓا۟ أَهْلَ ٱلْكِتَٰبِ إِلَّا بِٱلَّتِى هِىَ أَحْسَنُ إِلَّا ٱلَّذِينَ ظَلَمُوا۟ مِنْهُمْ ۖ وَقُولُوٓا۟ ءَامَنَّا بِٱلَّذِىٓ أُنزِلَ إِلَيْنَا وَأُنزِلَ إِلَيْكُمْ وَإِلَٰهُنَا وَإِلَٰهُكُمْ وَٰحِدٌۭ وَنَحْنُ لَهُۥ مُسْلِمُونَ ﴿٤٦﴾
And do not argue with the People of the Scripture except in a way that is best, except for those who commit injustice among them, and say, "We believe in that which has been revealed to us and revealed to you. And our God and your God is one; and we are Muslims [in submission] to Him."
Jews are People of the Book, owed courteous and respectful dealings.
Quran, Surah Al-Maaida 5:5
ٱلْيَوْمَ أُحِلَّ لَكُمُ ٱلطَّيِّبَٰتُ ۖ وَطَعَامُ ٱلَّذِينَ أُوتُوا۟ ٱلْكِتَٰبَ حِلٌّۭ لَّكُمْ وَطَعَامُكُمْ حِلٌّۭ لَّهُمْ ۖ وَٱلْمُحْصَنَٰتُ مِنَ ٱلْمُؤْمِنَٰتِ وَٱلْمُحْصَنَٰتُ مِنَ ٱلَّذِينَ أُوتُوا۟ ٱلْكِتَٰبَ مِن قَبْلِكُمْ إِذَآ ءَاتَيْتُمُوهُنَّ أُجُورَهُنَّ مُحْصِنِينَ غَيْرَ مُسَٰفِحِينَ وَلَا مُتَّخِذِىٓ أَخْدَانٍۢ ۗ وَمَن يَكْفُرْ بِٱلْإِيمَٰنِ فَقَدْ حَبِطَ عَمَلُهُۥ وَهُوَ فِى ٱلْءَاخِرَةِ مِنَ ٱلْخَٰسِرِينَ ﴿٥﴾
This day [all] good foods have been made lawful, and the food of those who were given the Scripture is lawful for you and your food is lawful for them. And [lawful in marriage are] chaste women from among the believers and chaste women from among those who were given the Scripture before you, when you have given them their due compensation, desiring chastity, not unlawful sexual intercourse or taking [secret] lovers. And whoever denies the faith - his work has become worthless, and he, in the Hereafter, will be among the losers.
Permissible food of the People of the Book may be eaten.
Sahih al-Bukhari 2004
Sahih... فأنا أحق بموسى منكم فصامه ...
"I am closer to Moses than you, so he fasted it and ordered that it be fasted."
Muslims honour Moses through the sunnah fast of Ashura.
Sahih Muslim 1134
Sahih... لئن بقيت إلى قابل لأصومن التاسع ...
"If I live until next year, I will certainly fast the ninth."
The Prophet ﷺ made the Muslim fast distinct from the Jewish one.
Sahih al-Bukhari 952
Sahih... إن لكل قوم عيدا وهذا عيدنا ...
"Every people has its festival, and this is our festival."
Muslims keep their own festivals.
Where the ruling is recorded
- al-Bahr al-Ra'iq, Kitab al-Siyar, Bab Ahkam al-Murtaddin. Honouring the festivals of non-Muslims endangers faith.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Sawm, the discussion of recommended and disliked fasts. Fasting Ashura alone is disliked because it resembles the Jewish fast; adding a day is recommended.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.