I volunteer for a Family History Society, now that I am retired.
The society is wholly run by volunteers, survives on donations and is a registered charity.
We currently have very old and slow broadband in a rural area at our HQ office, and are looking to upgrade to Fibre.
I doubt that BT offer a discount for charities, however, this is the residential forum, you need to ask on the business forum.
BT offers specific discounts and packages for registered charities, which can include reduced call rates and various benefits through the "Charities Club" contract. These discounts can be accessed when a charity contracts with BT for phone services or other offerings.
I have no idea if it covers Broadband.
It is a BT Business contract so you need to enquire there.