The Christmas tree is one of the symbols of the Christian festival and celebration; this is why it is named for Christmas. It is said that it was first officially used as a symbol in this manner in the sixteenth century in Germany, in the Cathedral of Strasbourg in 1539 CE.

It is not permissible to imitate the kuffaar in any of their acts of worship, rituals or symbols, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever imitates a people is one of them.” Narrated by Abu Dawood, 4031; classed as saheeh by al-Albaani in Irwa’ al-Ghaleel, 5/109

So it is not permissible to put up this tree in a Muslim house even if you do not celebrate Christmas, because putting up this tree comes under the heading of imitating others that is haraam, or venerating and showing respect to a religious symbol of the kuffaar.
What the parents must do is protect their children and keep them away from what is haraam, and protect them from the Fire as Allah, may He be exalted, says (interpretation of the meaning)”

“O you who believe! Ward off yourselves and your families against a Fire (Hell) whose fuel is men and stones, over which are (appointed) angels stern (and) severe, who disobey not, (from executing) the Commands they receive from Allaah, but do that which they are commanded”

[al-Tahreem 66:6]

It was narrated from Ibn ‘Umar (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “Each of you is a shepherd and each of you is responsible for his flock. The ruler of the people is a shepherd and is responsible for his flock. A man is the shepherd of his household and is responsible for his flock. A woman is the shepherd of her husband’s house and children and is responsible for her flock. The slave is the shepherd of his master’s wealth and is responsible for it. Each of you is a shepherd and each of you is responsible for his flock.”

Al-Bukhaari, 7138; Muslim, 1829.

Al-Bukhaari (7151) and Muslim (142) also narrated that Ma ‘qil ibn Yasaar al-Muzani (may Allah be pleased with him) said: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “There is no person whom Allaah puts in charge of others, and when he dies he is insincere to his subjects, but Allaah will forbid Paradise to him.”