CiviCRM is an open-source CRM that is specifically built for nonprofit and public sector use. There are no ongoing licensing fees, and it deeply integrates with Backdrop CMS (or can be run as a stand alone instance).

In a similar vein to Backdrop, it is deeply customizable. You can create any number of custom fields and forms to make sure you are tracking the data you need, and a variety of components that can be enabled as needed. This makes it suitable for more than just contact management. We've used it for membership management (including private members-only content on a site), events with registration, donations, searchable contact directories, and more.

In addition, because it's open-source and can be self-hosted, you have no vendor lock-in or surprise licensing fee increases. Privacy-wise, you own the data rather than entrusting it to a third-party or external entity, important for those who value data sovereignty and data portability.