Even with org.gnome.desktop.sound input-feedback-sounds = false, Chrome hangs (for me) when it calls the native file chooser.
This page gave me an idea:
which refers to the GTK_MODULES env variable. I am using Linux MATE, and its system-wide GTK_MODULES var = canberra-gtk-module. So I edited the /opt/google/chrome/google-chrome shell script (as root) and added this line:
near the top. Now run Chrome normally and the hang after file chooser problem is gone.
Based on what I read, canberra-gtk-module connects GTK apps like Chrome to event sounds. Apparently the file chooser can call an event sound which will or may work if GTK_MODULES var = canberra-gtk-module. Unsetting that env. var apparently should mean no event sounds when using Chrome. I never heard such sounds before with the file chooser, but there are still event sounds with when adjusting volume, and video sound still works fine. So I don't really understand why the freeze happens; I'm guessing it's not a Chrome problem.
The above is not a great solution though, since that shell script can get replaced by an update.
Note: I didn't try installing xdg-desktop-portal-gnome because MATE doesn't use Gnome-shell and it would have installed a bunch of packages I didn't want in MATE.