This [questioner] says:
As-salām ʿAlaykum. [My] non-muslim relatives come together for the celebration of new year. So is it permissible for us to meet with them on that day just for greetings, on the basis of preserving the ties of kinship.
The answer summarily is NO. Do not meet with them on this day because it is a festival to them. If it is so required of you, then go to them before that before that new year [celebration], or after it has ended. And it is not imperative that you reach out to them physically. Calling them [on phone] suffices, with effort on daʿwah [calling them to the path of Allāh] and calling them to guidance. And when Allāh makes it easy for you to visit them when they are not doing this celebration, or this get-together. Because this companionship may be taken for affirmation [from you] for the likes of this celebration and festival that is not from the festivals of the people of Islām.
So, If you want to preserve your ties of kinship, you must preserve it in accordance to the Islamic legislation. This principle does not differ for a small or big thing.
“O Abū ʿAbdir-Raḥmān, we do not intend except good. He [ʿAbdullāh bn Masʿūd] said: How many intends good but is not successful with it!”
And before that he said: “[Either] You are upon a path that is more correct than the path of the companions of Muḥammad ﷺ or you are opening a door of misguidance.”
Just [one of] two [things] no third. They said: “we intended good”. [He replied]: “How many intends good but is not successful with it” This is the answer.
[They say it is] just to preserve ties of kinship. Yes, we support preserving ties of kinship. [But] preserve them in accordance to the Islamic legislation. Is it not the Islamic legislation that urged you to preserving [ties of kinship]? Therefore, stick to the Islamic legislation in how you preserve [the ties].