This actually works fine.  Try these slightly modified steps:

1 Open Metadata Editor. 
2 Double-click a field (except Genre) to open it for editing.
3 Enter "asdf 1234 zxcv" into the field
4 Double-click the "1234" part to select it
3 Right-click the field. The field (and any text in it that was selected) becomes deselected.

But, go ahead and select "Cut" from the popup menu. You'll see that the "1234" is actually cut as it should be.

So, what this bug should really be for is a visual, not functional, problem.

(In reply to Leland Lucius from comment #1)
It works for me too, but as you noted it "looks" like the selection is lost.

I'll update the bug description from:
"Linux: Metadata Editor fields except Genre lose selection on right-click."
to:
"Linux: Metadata Editor fields appear to lose selection on right-click."

I'll also update the steps to reproduce.

Works for me with Audacity 3.0.2 and 3.0.4 alpha.