All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If you mean by the “religion of Christians” the Message that was brought by ‘Eesa (Jesus) then, it is impermissible to do so. Moreover, it is an act of disbelief. It is impermissible to curse any previous religion which was brought by the Prophets of Allaah. The religion of all the Prophets is one; the Muslims believe in all the Prophets.
Allaah The Almighty Says (what means): {The Messenger has believed in what was revealed to him from his Lord, and [so have] the believers. All of them have believed in Allaah and His angels and His books and His messengers, [saying], "We make no distinction between any of His messengers."} [Quran 2:285]
Blaspheming, insulting or mocking any of these religions is considered an act of disbelief. Allaah The Almighty Says (what means):
• {Say, "Is it Allaah and His verses and His Messenger that you were mocking?"* Make no excuse; you have disbelieved after your belief.} [Quran 9:65-66]
• {He has ordained for you of religion what He enjoined upon Nooh (Noah) and that which We have revealed to you, [O Muhammad], and what We enjoined upon Ibraaheem (Abraham) and Moosa (Moses) and ‘Eesa (Jesus) - to establish the religion and not be divided therein.} [Quran 42:13]
If you mean by “religion” the innovated and distorted religion of the Christians which involves Shirk (polytheism) and superstitions; then, it is permissible to curse this religion and describe those who embrace it as polytheists and disbelievers.
Allaah The Almighty Says (what means): {They have certainly disbelieved who say, "Allaah Is the third of three."} [Quran 5:73]
However, if this cursing leads them to curse Islam or its Prophet, sallallaahu ‘alayhi wa sallam, then, it is impermissible to do this act in order to eliminate the means leading to unfavorable results. Allaah The Almighty forbade insulting the polytheists’ idols in order not to lead to insulting Allaah The Almighty. Allaah The Almighty Says (what means): {And do not insult those they invoke other than Allaah, lest they insult Allaah in enmity without knowledge.} [Quran 6:108]
Allaah Knows best.