Should I fully Respect my non-Shia Parents?

It is obligatory for children to observe two things towards their parents - even if they are not non-Shia parents or not Muslims :

Goodness to them by paying their living expenses if they are in need, and fulfilling other requests in accordance with the affairs of conventional and usual life and according to what a healthy nature requires. Of course, this is something that will be different according to their differences. In this article we go see what Islam talks about this:

Companionship with them for good; It means that a child should not do bad things to his parents either in speech or in deed, although they have wronged him; because it is stated in the narration:

"Even if they hit you, don't be angry with them and say: Ghofer Allah Lakma (may God have mercy on you)". [1]

What was said has nothing to do with the religion of the parents, Of course, except for the cases where the parents order the child to give up his religion or do something contrary to Islamic teachings, in which case, in verses such as verse 8 of Surah Ankabut and verse 15 of Surah Luqman, the Qur'an explicitly commands not to follow them.

Qur'an says;

“We have enjoined on man kindness to parents….”[2] 

And in another verse;

“But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness[3]

       In the following, it should be said; It is natural to respect parents regarding the question that if a Shia person has parents who are Muslim; but they follow the Sunni religion; it has more appearance and occurrence, in addition to the fact that there are also certain traditions in this case:

The narrator says:

 I heard a man saying to Imam Sadiq (AS): My parents are against the right religion (Shia) (what should I do with them?), His Holiness said:

"Do good to them as if you do good to Muslims who have accepted our province". [4]

In other words, the religion of your parents should not affect the way you treat them.

In another narration, Muammar bin Khalad asks Imam Reza (A.S):

Can I pray for my parents who were not Shia and followers of Haqq (truth)? His Holiness replied:

"Yes sir! Pray for them and give them charity and if they are alive, be patient with them, because the Messenger of God said:

God sent me for mercy,  not for Ingratitude".[5]

  In this regard, even if the parents are Nasbi (enemies of Ahl al-Bayt), it is still necessary to respect them:

Ali bin Mahziar narrates from Bakr bin Saleh who said:

One of my sons-in-law wrote a letter to Imam Jawad (A.S) that my father was a nasbi person and had a very bad opinion and I am in discomfort because of him, If you think it is good, pray for me, and also your opinion about whether I should express my enmity with his or whether I should continue to tolerate him, What is?! In response, Imam wrote:

I noticed what you wrote in your letter and if God wills, I will never stop praying for you, (But regarding your father) tolerance is better than enmity!

[6] 

References:

[1]"Living with non-Muslim parents", 31442.

[2] Surah Ankabut (29:8) وَوَصَّيْنَا ٱلْإِنسَـٰنَ بِوَٰلِدَيْهِ حُسْنًۭا

[3] Surah Luqman(31:15) وَإِن جَـٰهَدَاكَ عَلَىٰٓ أَن تُشْرِكَ بِى مَا لَيْسَ لَكَ بِهِۦ عِلْمٌۭ فَلَا تُطِعْهُمَا

[4] Kilini, Muhammad bin Yaqub, Kafi, Mohaghegh, Corrected, Ghafari, Ali Akbar, Akhundi, Muhammad, Vol. 2, p. 162, Tehran, Dar Al-Katb al-Islamiyya, 4th edition, 1407 AH.

[5] The same, vol. 2, p. 159.

[6] Sheikh Sadouq, Amali, p. 191, Beirut, Alami, fifth edition, 1400 AH.