Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
1- Holding a fundraiser during Friday khutbah would be forbidden as it takes away from the goal and purpose of the Khutbah and it would lead to people stepping over the worshippers and this is forbidden.
2- There is no harm in the Khateeb asking for donations during the khutbah but then not being collected until after the Khutbah.
In responding to your question about holding a fundraiser during Friday khutbah, Dr. Waleed Al-Maneese, a Senior Member of the Permanent Fatwa Committee of the Assembly of Muslim Jurists in America (AMJA), states:
It seems that holding a fundraiser during Friday khutbah would be forbidden as it takes away from the goal and purpose of the Khutbah. It would also lead to people stepping over the worshippers to distribute the fundraising material and this act of stepping over others during the Friday Prayer is forbidden.
As an alternative, there is no harm in the Khateeb asking for donations during the khutbah but then not being collected until after the Khutbah. Alternatively, they could have the fundraising before the khutbah begins.
Almighty Allah knows best.
Source: www.amjaonline.net