Access is the defacto option for creating DBs with forms for user input, but there are other solutions that can be created.
I haven't used any myself, but from a google search:
http://www.vfront.org/ - Web frontend for PostgreSQL
Ok. Here is probably some helpful info for you:
If you a registered 501c3 non-profit you qualify for non-profit pricing from Microsoft. If you don't need office applications you can get email and online versions of apps completely free. If you need the Office suite the cheapest option I think starts at $3/month.
If you don't know about TechSoup, go there (techsoup.org) and register. You can get Microsoft products, in particular, for way under normal resale value. Office Standard 2019 is listed at $39 right now.
Online versions of MS apps and the Office 365 version of the Office suite apps include the ability to do live collaboration if you store your files in SharePoint or OneDrive. So if you have a single Excel file, multiple people can access it and edit it all at once. It might be best to keep people on their own sheets and consolidate later, but that's a process thing you'll have to work out.
I don't think I would personally go with an Access database just b/c they are a bit antiquated. There might be some kind of pre-built open source or cheap option for your needs depending on what all you need to be able to store and retrieve for your "database." Something with a web front end for entry and retrieval would probably be easy enough to find or build. I'm not a DB guy so I don't have a bunch of tools that I know of off the top of my head,, but building something on top of a real DB like MySQL or MS SQL (even SQL Express) would be far more scalable in the long term, offer more features, and probably be more reliable.
Here are a few things that came up with a quick search:
Linux is more secure than OSX or Windows, both because it is designed in a superior way, and because its marketshare is small, so there are the fewest attempts to penetrate it. It has none of the built-in telemetry or other unwanted monitoring stuff that is in Windows either.
https://appdb.winehq.org/objectManager.php?sClass=application&iId=337
WINE is built into Mint and Ubuntu and allows you to run Windows and Apple software natively. It looks like depending on the version, you could perhaps continue using Filemaker.
If that isn't an option, you could look at the options here: https://alternativeto.net/software/filemaker-pro/?platform=linux
This one looks promising maybe - http://www.vfront.org/
One bonus of Linux is that there are MANY Free Open Source softwares for it.