Imaam al-Bukhaari (may Allaah have mercy on him) gave one of the chapters in his Saheeh the title of “Baab qabool al-hadiyah min al-mushrikeen (Chapter on accepting gifts from the polytheists),” under which heading he listed a number of ahaadeeth indicating that this is permitted.
Al-Haafiz Ibn Hajar commented: “On this topic, Abu Dawood and al-Tirmidhi narrated from ‘Ayyaad ibn Himar [??] who said: ‘I gave the Prophet (peace and blessings of Allaah be upon him) a gift of a she-camel. He asked me, “Have you become Muslim?” I said, “No.” He said, “I have been forbidden to accept the gifts of the mushrikeen.”’ Then al-Haafiz (may Allaah have mercy on him) quoted some of the comments made by the scholars to reconcile the texts which indicate that such gifts should be refused with those which indicate that they should be accepted. (The scholars said that) gifts should be refused when the intention behind them is to win the Muslim over (by softening his heart towards them), and they should be accepted when by doing so there is the hope of befriending that person and opening his heart to Islam.
There is nothing wrong with accepting unsolicited gifts and donations from non-Muslims, and it is permissible to spend them on Islamic projects and in other ways.
But asking for donations from non-Muslims carries several risks, such as being humiliated in front of them or being controlled by them.
If there is no danger of such things happening, there is nothing wrong with asking. When he was still in Makkah, the Prophet (peace and blessings of Allaah be upon him) used to ask for help for the sake of da’wah, without any humiliation involved, from some of the mushrikeen, such as his uncle Abu Taalib and others. There is no humiliation involved in putting out charity boxes or circulating flyers giving account numbers for donations, and so on. And Allaah knows best.