Free and Open Source Software
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I also use this one and it's sooo well done. I recommend it too.
Quote, I'm using tasks.org synced over Nextcloud (supported by davx5 on android or natively on iOS).
Nextcloud Tasks?
Nextcloud is nice since iPhone natively supports caldav/carddav so you can use the built in reminders app.
Joplin may be an option
I love joplin, its so simple and intuitive. I also use it to produce simple manuals and documentation for my code.
It’s the best option I’ve found. Plus the fact that it’s easy to synchronize between iOS, windows and Linux is amazing.
I use Tasks for to dos. Joplin is great for notes, and I use that too for notes.
Orgzly app for android. It is based on org-mode plain text files and support sync via WebDav. Org-mode is one of the oldest format of todo files and have a huge community/plugins/guides/etc.
Because it is plain text in very popular format it may be easily migrated between different cloud storages and may be edited from PC tooo in a any text editor.
Also format of org files is human readable.
I don't know what features you're looking for but I use nextcloud notes. It's really great for my uses, I keep categorized shopping lists, to do lists, email drafts, etc all in one app. I can access it trough the Android app on my phone and through the web frontend on my nextcloud instance from anywhere.
Vikunja (hosted on tchncs: https://todo.tchncs.de/) is great for tasks but I haven't tried using it for a grocery list.
Vikunja is very slick!
This is not strictly a to-do list app but a Kanban board. It has many of the same features and It work really well. The api is also amazing if you want other apps to work with it (doing some programming yourself tho)
Quillpad has an experimental sync option for nextcloud, although I perfer keeping it disconnected from the network, and you can make checklists as well.
I've been trying out Carnet for a few days, syncs with Nextcloud and has an app for the dashboard and a mobile app for android.
So far I like it, a little clunky in some ways, but overall solid and looks nice.
You can just use plain todo.txt. I wrote an extension for it as well, but it's a bit niche for a certain type of users: https://proycon.anaproy.nl/posts/todo/
I don't think it's open source but we use our groceries. Just links to an email only no password. They just send you a code when you link the email to a new app. It's also cross platform if that matters at all. Also requires no permissions granted to run and only requests a camera permission to scan barcodes.
I use carnet off of fdroid