In fact cmd-H does hide the application. However it also opens the manual (file://localhost/Applications/Gnucash.app/Contents/Resources/en.lproj/Gnucash%20Guide/index.html). So it is still true that "there is no way to hide the application with a single key press" in the sense that one must close the browser tab where the manual has opened.

I note this bug is coming up on two years old. Seems to me it shouldn't take two years to fix.

Yeah, that's what I said.

In fact it's so easy to fix that you can do it yourself: Make sure GnuCash isn't running, then edit $HOME/Library/Application Support/Gnucash/accelerator-map. TextEdit will work fine as an editor. You may need to enable "Show Library Folder" in Finder's View Options when visiting your home folder (the one with the same name as your userid) to navigate to it.
Search for "HelpTutorialAction" (it should be line 169). Remove the ';' from the beginning and the <Primary>h from between the quotes at the end. Save the file as plain text. When you restart GnuCash command-h will no longer open help.
Of course if help is already open in the browser it will stay open; I know of no way to get the browser to close it from inside GnuCash.

I've also made that change to the accel-map that's included with GnuCash, but that will only affect new installations; it won't overwrite the file you already have in case you've made other customizations.

Thanks, that works. (Although it was line 185 in my case.)

GnuCash bug tracking has moved to a new Bugzilla host. This bug has been copied to https://bugs.gnucash.org/show_bug.cgi?id=733164. Please update any external references or bookmarks.