All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ʻalayhi wa sallam, is His slave and Messenger.
The Islamic Shariah allows kindness to non-Muslims; Allah, the Exalted, says (what means): {Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.} [Quran 60:8]
Such kindness is emphasized towards the non-Muslim who has other rights over the Muslim such as being a neighbor, a relative, a neighbor of one's parents, and the like. However, while showing kindness to the non-Muslim, the Muslim must be careful to avoid what may lead to having affection for him, which is forbidden by the Shariah.
Shaykh Ibn ʻUthaymeen was asked, “I have a Christian neighbor whom I have invited to Islam more than once, but he refused and persistently adhered to his religion believing it to be the true religion. Do I bear a sin for talking to him and keeping his company? What are my duties towards him?”
Answer:
“Allah, the Exalted, says (what means): {You will not find a people who believe in Allah and the Last Day having affection for those who oppose Allah and His Messenger...} [Quran 58:22] It is impermissible for a Muslim to seek the means that lead to having affection towards a non-Muslim, because this would be considered seeking what negates his belief in Allah, either partially or completely. However, if the non-Muslim greets us, we greet him back with a like greeting, and we do not mistreat a non-Muslim neighbor, because the Prophet, sallallahu ʻalayhi wa sallam, said, ‘He who believes in Allah and the Last Day should honor his neighbor.’
The scholars said that neighbors are classified into four categories:
First, a neighbor who is a Muslim relative; and he has three kinds of rights: the rights of a Muslim, the rights of a relative, and the rights of a neighbor.
Second, a neighbor who is a non-Muslim relative; and he has two kinds of rights: the rights of a neighbor and the rights of a relative.
Third, a Muslim neighbor who is not a relative; and he has two kinds of rights: the rights of a Muslim and the rights of a neighbor.
Fourth, a non-Muslim neighbor who is not a relative; and he has one kind of rights: the rights of a neighbor.
The Prophet, sallallahu ʻalayhi wa sallam, said, ‘He who believes in Allah and the Last Day should honor his neighbor.’
Honoring one's non-Muslim neighbor does not necessarily entail having affection for him. It often happens that a person honors a guest or someone whom he met after a long travel, so he honors him and prepares a generous meal for him while he does not genuinely like him. As for affection and expressing what leads to it towards a non-Muslim, this undermines one's faith.”
So if you fear that inviting them might lead to this prohibited affection, it is better to avoid it and to show kindness to them in other ways.
Lastly, you should beware of violations of the Shariah in your parties, such as prohibited signing, music, free intermixing between men and women, and the like of Shariah violations that are often committed in many parties in our present time.
Allah knows best.