St. Hubertus and Ethical Hunting.

A little bit of trivial I found in my surfing while learning about the significance of this symbol, which relates to Saint Hubert of Liège who is the patron saint of, among other things, archers, dogs, forest workers, and hunters:

Sankt Hubertus (German) is honored among sport-hunters as the originator of ethical hunting behavior. During Hubert's religious vision, the Hirsch is said to have lectured Hubertus into holding animals in higher regard and having compassion for them as God's creatures with a value in their own right. For example, the hunter ought to only shoot when a humane, clean and quick kill is assured. He ought shoot only old stags past their prime breeding years and to relinquish a much anticipated shot on a trophy to instead euthanize a sick or injured animal that might appear on the scene. Further, one ought never shoot a female with young in tow to assure the young deer have a mother to guide them to food during the winter. Such is the legacy of Hubert who still today is taught and held in high regard in the extensive and rigorous German and Austrian hunter education courses.

Christian cross seen between the antlers of a stag. This image is a reference to the two Christian patron saints of hunters, Saint Hubertus and Saint Eustace, both of whom converted to Christianity after experiencing a vision in which they saw a Christian cross between the antlers of a stag.
This symbol is also found on the  Jägermeister liquor label also features the following verse from the poem Weidmannsheil, by the forester, hunter, and ornithologist Oskar von Riesenthal (1830–1898).

Das ist des Jägers Ehrenschild,
daß er beschützt und hegt sein Wild,
weidmännisch jagt, wie sich’s gehört,
den Schöpfer im Geschöpfe ehrt.

According to Mast-Jägermeister SE, the translation is:

It is the hunter’s honour
that he Protects and preserves his game,
Hunts sportsmanlike,
honours the Creator in His creatures.

A loose translation which preserves the rhyme and meter is:

This is the hunter’s badge of glory,
That he protect and tend his quarry,
Hunt with honour, as is due,
And through the beast to God is true.

Interesting as all this is, it doesn't answer my question of why this symbol is also found on some German hiking badges.  But, the stuff about ethical hunting was pretty interesting.