Can You Backbite a Non-Muslim?
Question

Please inform us if the Ghibah (backbiting) is the same for non-believers as it is for Muslims.
Praise be to Allah.Importance of politeness in Islam
It is not a Muslim characteristic to speak rudely. The Prophet (peace and blessings of Allah be upon him) said: “The Muslim does not slander, curse, speak obscenely or speak rudely.” (Narrated by At-Tirmidhi). 
Whoever does a thing a lot, it will become his habit, so the Muslim should keep away from all the ways that lead to evil, whether minor or major. Whoever drives his sheep near the enclosure of the king is bound to cross the line. 
Can You Backbite a Non-Muslim?
If your question is referring to backbiting a non-Muslim by mentioning his physical defects, such as his having a long nose or a big mouth, etc., then do not do this, because this is making fun of the creation of Allah.
If it means talking about his bad characteristics which he flaunts openly, such as adultery and immorality, or drinking alcohol, and warning against him, there is nothing wrong with that. 
Scholarly opinions on backbiting Non-Muslims
There follow some of the comments of the scholars on this topic.
 Zakariya Al-Ansari said: 
“Backbiting a non-Muslim is impermissible if he is a Dhimmi [a non-Muslim living under Islamic rule], because that puts them off from accepting the Jizyah (type of tax) and it is going against the treaty of Dhimmah (agreement between non-Muslim subjects and the Islamic state) and the words of the Prophet (peace and blessings of Allah be upon him). ‘Whoever makes a snide comment to a Dhimmi has earned Hell.’ (Narrated by Ibn Hibban in his Sahih)
 It is permissible to backbite a non-Muslim if he is a Harbi (one who is at war with the Muslims), because the Prophet (peace and blessings of Allah be upon him) used to command Hassan to lampoon the pagans.” (Asna Al-Mutalib Ma`a Hashiyatihi, vol. 3, p. 116)
Ahmad ibn Hajar Al-Haythami said in Az-Zawajir `an Iqtiraf Al-Kaba’ir: 
“Al-Ghazali was asked about backbiting a non-Muslim. He said: with regard to a Muslim, it is forbidden for three reasons: causing offence; criticising the creation of Allah, for Allah is the Creator of the deeds of His slaves; and wasting time in something that is of no benefit. The first is prohibited, the second is (disliked), and the third is not the best thing that one can do. 
With regard to the Dhimmi, he is like the Muslim as far as not harming him is concerned, because the Lawgiver protects his honour, blood and property. It was said in Al-Khadim, the first view is correct. 
Ibn Hibban narrated in his Sahih that the Prophet (peace and blessings of Allah be upon him) said, ‘Whoever makes a snide comment to a Jew or a Christian deserves Hell.’ 
The meaning of making a snide comment is to make someone hear something that will cause offence to him. There is no stronger evidence than this, i.e., it is prohibited. 
Al-Ghazali said: with regard to the Harbi, the former is not prohibited, and the second and third are disliked. 
With regard to one who commits an innovation (Bid`ah), if he becomes a non-Muslim thereby, then he is like a Harbi, otherwise he is like a Muslim, but speaking of him with regard to his Bid`ah is not disliked. Ibn Al-Mundhir said, concerning the words of the Prophet (peace and blessings of Allah be upon him), “It is your mentioning about your brother that which he dislikes,” – this indicates that in the case of one who is not your brother, such as a Jew or a Christian or a follower of any other religion, or one whose Bid`ah has put him beyond the pale of Islam, there is no backbiting in his case.” 
 And Allah knows best.