My dconf/gsettings installation is broken. How can I fix it without Ubuntu reinstall?

This can also happen if you have PATH conflicts with a Python enviroment manager like Anaconda.

Make sure to run which gsettings before getting too deep. If that doesn't print /usr/bin/gsettings and instead something like /home/{username}/anaconda3/bin/gsettings you probably have something .profile/.bashrc/.zshrc like:

export PATH=$HOME/anaconda3/bin:$PATH

Change it to:
export PATH=$PATH:$HOME/anaconda3/bin

Appending instead of preprending to the PATH variable will solve your issue, but be aware that anything in your system bin, or other PATH locations, will supersede your anaconda3/bin.

Another option would be to alias /usr/bin/gsettings:

alias sys-gsettings=/usr/bin/gsettings
sys-gsettings get org.gnome.todo view

I've found the solution. It appears that I got several custom-built libraries in /usr/local/lib that "shadowed" system libraries from /usr/lib/x86_64-linux-gnu/.

I discovered it by checking dynamic libraries loaded by libdconfsettings.so:

ldd /usr/lib/x86_64-linux-gnu/gio/modules/libdconfsettings.so

...
<  several dynamic libraries from /usr/local/lib >
...

It happened because of the order of search paths for dynamic libraries (defined in /etc/ld.so.conf.d/). The order was the following:

1. /lib/i386-linux-gnu
2. /usr/lib/i386-linux-gnu
3. /lib/i686-linux-gnu
4. /usr/lib/i686-linux-gnu
5. /usr/local/lib
6. /lib/x86_64-linux-gnu
7. /usr/lib/x86_64-linux-gnu

So if for example you put your own libc.so into /usr/local/lib it will be loaded instead of default libc.so from /lib/x86_64-linux-gnu.

The fix:

sudo mv /etc/ld.so.conf.d/libc.conf /etc/ld.so.conf.d/xuserlocal.conf
sudo ldconfig
sudo reboot