How to open context menu in (MacOS) Finder with keyboard

Short answer: no.

Most items in the Finder’s context menu are already accessible via the menu bar & any thing in the menu bar is fair game for a custom keyboard shortcut in System Preferences (System Preferences > Keyboard > Keyboard Shortcuts > Application Shortcuts). You can assign keyboard shortcuts for most apps (Firefox excluded) in that panel and that includes the Finder. If it doesn’t immediately take effect, just relaunch the Finder.

Quicksilver proxy objects, specifically the "Current Selection" proxy object.

This will let you invoke Quicksilver with all of the items you have selected in the Finder as the thing you do stuff to.

I have a trigger (mine's set to ⌘+shift+space) set up to get all the currently-selected items in the Finder. The end result is that I can perform actions on the currently-selected items in the Finder with, like, three keystrokes. Most of the things I can do to the items are in the context menu, but not all, if I recall. Still, pretty handy.

Not quite exactly the context menu, very close however. If you use the commands for Universal Access you can get to the menu for the Task button in the buttonbar.

Press control-F5 to put the focus on the buttonbar. Press tab until the Task button is highlighted, press space to open it, use the arrows to make your selection.

Note that you may have to enable Universal Access, and that you can change the control-F5 shortcut in the Keyboard prefpane. Also, the name of the button may be slightly different in English (I'm running in Dutch, and can't be bothered to switch languages to check the exact translation).