It is permissible to have iftaar with non-Muslims if there is a shar’i reason for doing so, such as calling them to the true religion, or softening their hearts towards Islam, etc, which are what is hoped for if they come and eat iftaar at the tables set up for communal iftaar, as happens in some countries. But if it is done just to be friendly towards them and enjoy their company, this is a dangerous matter, because the principle of al-wala’ wa’l-bara’ (befriending the believers and showing enmity towards the disbelievers) is one of the basic principles of Islam, and one of the most important duties of the believers. This principle is referred to in a number of verses in the Book of Allaah and ahaadeeth of the Prophet (peace and blessings of Allaah be upon him), for example: 

Allaah says (interpretation of the meaning): 

“You (O Muhammad) will not find any people who believe in Allaah and the Last Day, making friendship with those who oppose Allaah and His Messenger (Muhammad), even though they were their fathers or their sons or their brothers or their kindred (people). For such He has written Faith in their hearts, and strengthened them with Rooh (proofs, light and true guidance) from Himself. And He will admit them to Gardens (Paradise) under which rivers flow, to dwell therein (forever). Allaah is pleased with them, and they with Him. They are the party of Allaah. Verily, it is the party of Allaah that will be the successful”

[al-Mujaadilah 58:22] 

“O you who believe! Take not for Awliyaa’ (protectors or helpers or friends) disbelievers instead of believers. Do you wish to offer Allaah a manifest proof against yourselves?”

[al-Nisa’ 4:144] 

“O you who believe! Take not the Jews and the Christians as Awliyaa’ (friends, protectors, helpers), they are but Awliyaa’ of each other. And if any amongst you takes them (as Awliyaa’), then surely, he is one of them. Verily, Allaah guides not those people who are the Zaalimoon (polytheists and wrongdoers and unjust)”

[al-Maa'idah 5:51] 

“O you who believe! Take not as (your) Bitaanah (advisors, consultants, protectors, helpers, friends) those outside your religion (pagans, Jews, Christians, and hypocrites) since they will not fail to do their best to corrupt you. They desire to harm you severely. Hatred has already appeared from their mouths, but what their breasts conceal is far worse. Indeed We have made plain to you the Ayaat (proofs, evidences, verses) if you understand”

[Aal ‘Imraan 3:118] 

Based on this, the ruling on gathering with these people for iftaar depends on the intention. And Allaah knows best.