Is it Obligatory for Parents to Teach Islamic Rules to their Children?

Learning and raising a child is one of the duties of parents, which includes teaching them Islamic rules; therefore, it is necessary for them to either take action on this matter themselves or provide the ground for them to learn it from others - for example, by participating in the relevant classes - and if they fail in this matter, they will be guilty.

The answer of the offices of the supreme authorities of Taqlid regarding this question is as follows: [1]

Ayatollah Khamenei:

It is obligatory to teach those who are ignorant of the rulings.

Ayatollah Shabiri Zanjani

If they failed to teach him the rules; They have committed a sin.

 Ayatollah Alawi Gorgani :

According to some traditions, parents who do not teach their children the rules and do not provide the basis for their education and are lax will be punished on the Day of Judgment and in some cases will be punished.

Ayatollah Makarem Shirazi :

It is obligatory for the father and mother to make serious efforts in the direction of correct education and upbringing of the child and familiarize him with religious duties.

Therefore, if they fail to fulfill their duty, they are guilty.

Reference:

[1] Transferred from the offices of Ayat-e-Azam: Khamenei, Shabiri Zanjani, Alavi Gorgani, Makarem Shirazi (Zolham al-Ali) by the Islam Quest site.