Short answer
Not to the church's worship or religious mission: funding services, building a church or missionary work is haram. Voluntary charity through a church-run food bank, shelter or relief appeal that feeds and houses people in need is allowed, as long as it is not your zakat. Giving to the people directly or to a non-religious charity is simplest.
Helping the religious activities of another faith is haram, since the Quran forbids cooperating in sin; Hanafi texts treat a Muslim's bequest to build a church or temple as void. Voluntary sadaqa to non-Muslims in need is permitted and rewarded. Zakat may not be given to non-Muslims in the Hanafi school.
The four schools agree on this.
Explanation
The Quran's rule is: cooperate in righteousness and piety, and do not cooperate in sin. Feeding the hungry is righteousness wherever it happens. Paying for worship directed to other than Allah, or for efforts to draw people away from Islam, is not.
- Allowed: food banks, homeless shelters, disaster appeals and hospital funds run by churches, when the money goes to people in need. The Prophet ﷺ said there is reward in serving every living creature.
- Not allowed: the collection plate during a service, building and roof funds, missions and evangelism, and buying religious materials.
- Not zakat: zakat goes to Muslims in need through proper channels. See can zakat be given to non-Muslims.
Common situations: a church bake sale for the building fund is best avoided, while one for a children's hospital is fine. If a neighbour's family is raising money for an operation through their church, give to the family directly. If you are unsure how a charity uses its funds, ask, or choose a secular or Muslim charity that does the same work.
Muslims are known for giving. Showing it across faith lines, through help for neighbours and relief work, is a beautiful thing. See charity to non-Muslims and zakat and sadaqah.
The evidence
Quran, Surah Al-Maaida 5:2
يَٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوا۟ لَا تُحِلُّوا۟ شَعَٰٓئِرَ ٱللَّهِ وَلَا ٱلشَّهْرَ ٱلْحَرَامَ وَلَا ٱلْهَدْىَ وَلَا ٱلْقَلَٰٓئِدَ وَلَآ ءَآمِّينَ ٱلْبَيْتَ ٱلْحَرَامَ يَبْتَغُونَ فَضْلًۭا مِّن رَّبِّهِمْ وَرِضْوَٰنًۭا ۚ وَإِذَا حَلَلْتُمْ فَٱصْطَادُوا۟ ۚ وَلَا يَجْرِمَنَّكُمْ شَنَـَٔانُ قَوْمٍ أَن صَدُّوكُمْ عَنِ ٱلْمَسْجِدِ ٱلْحَرَامِ أَن تَعْتَدُوا۟ ۘ وَتَعَاوَنُوا۟ عَلَى ٱلْبِرِّ وَٱلتَّقْوَىٰ ۖ وَلَا تَعَاوَنُوا۟ عَلَى ٱلْإِثْمِ وَٱلْعُدْوَٰنِ ۚ وَٱتَّقُوا۟ ٱللَّهَ ۖ إِنَّ ٱللَّهَ شَدِيدُ ٱلْعِقَابِ ﴿٢﴾
O you who have believed, do not violate the rites of Allah or [the sanctity of] the sacred month or [neglect the marking of] the sacrificial animals and garlanding [them] or [violate the safety of] those coming to the Sacred House seeking bounty from their Lord and [His] approval. But when you come out of ihram, then [you may] hunt. And do not let the hatred of a people for having obstructed you from al-Masjid al-Haram lead you to transgress. And cooperate in righteousness and piety, but do not cooperate in sin and aggression. And fear Allah; indeed, Allah is severe in penalty.
Muslims help good causes but not the worship of other than Allah.
Quran, Surah Al-Mumtahana 60:8
لَّا يَنْهَىٰكُمُ ٱللَّهُ عَنِ ٱلَّذِينَ لَمْ يُقَٰتِلُوكُمْ فِى ٱلدِّينِ وَلَمْ يُخْرِجُوكُم مِّن دِيَٰرِكُمْ أَن تَبَرُّوهُمْ وَتُقْسِطُوٓا۟ إِلَيْهِمْ ۚ إِنَّ ٱللَّهَ يُحِبُّ ٱلْمُقْسِطِينَ ﴿٨﴾
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.
Good done to peaceful non-Muslims is allowed.
Sahih al-Bukhari 2363
Sahih... في كل كبد رطبة أجر ...
"There is a reward for serving every living being."
Charity to anyone in need is rewarded.
Where the ruling is recorded
- al-Hidaya, Kitab al-Wasaya, the chapter on bequests of non-Muslims. A bequest to build a church is invalid from a Muslim.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.