contextual menucustomizationfinderfinder-tagshortcut-menu
When I right-click an item in Finder, the context menu has a Tags section containing colored tags:
Tags…
In previous versions of macOS / OS X, the section was called "Labels".
I don't use Tags in Finder, so the Tags section adds 3 vertical menu items of wasted space. The colored tag dots also stretch small menus pretty far to the right.
Is there any way to hide the Tags section when right-clicking files and folders in Finder?
My own experience (on 10.9) is that the service uses the default search engine selected for the default browser, so right now my own "Search with…" says "Search DuckDuckGo for…" and will open in Firefox.
This doesn't answer your other questions, but it may mean you don't need to bother. I hope it helps. I've an old system running 10.6 so I'll give that a look when I get a chance and see if the same can be done there.
If you go to Preferences -> Extensions -> Finder, you will see the Finder extension that you can enable/disable and you can enable/disable the Finder extension from the Dropbox app itself.
Unfortunately I don't believe you can simply remove the one option but rather it's an all-or-nothing scenario based on the extension itself. Well, at least until Dropbox makes some improvements.
Best Answer
Finder > Preferences > Tags
you'll see the text:
Drag the tag dots out of the bottom "Favorite Tags" section.
If you remove all of the Favorite Tags, the Tags menu will be hidden from Finder right-click context menus.