Islam is all for treating our parents, relatives and friends compassionately. As a Muslim/ah, it is your duty to be most gentle and kind to them, especially your parents. Allah says, (Keep their company with kindness in this world, and follow the path of him who turns to Me. Then unto Me will you return, and I shall tell you what you did.) (Luqman 31: 15)
Keeping good company of one's parents includes accepting their invitations, eating with them all foods that are permissible for us to consume, which excludes pork, intoxicants, and that which has been immolated to idols.
You are allowed to participate in the festivities of Christmas or holiday seasons on condition that you abstain from specific religious rituals associated with them, if any. As Muslims we revere Jesus (peace and blessings be upon him) as one of the mighty messengers of Allah; we would have certainly celebrated the same, if only it had been a tradition established by Jesus and his authentic disciples. We certainly know that was not the case. It is all too well known that celebration of Christmas was introduced into Christianity in the manner of the pagan cultic rituals prevailing in the lands that the Christians conquered and as such, it is not something to be cherished as an authentic Christian festival.
Muslims refuse to deify not only Prophet Jesus (peace and blessings be upon him) but anyone else for that matter including Prophet Muhammad (peace and blessings be upon him). We believe in all prophets, and consider them all as preaching the same essential message: Do not worship any other gods but Allah. It would certainly be a good idea for you to broach this topic with your parents in one of their gentler moments.