The key part is

Will mir die Hand noch reichen,
Derweil ich eben lad'.
"Kann dir die Hand nicht geben,..."

This means: Comrade, since you are giving your life for our just cause, my best service to you is to continue fighting for it, just as I would have expected if it were the other way round.

In other words, the song is about a justified war, fought by convinced volunteers. Uhland and his early readers believed this to be the case when defending their countries against invadors. Those who sing or play it later, implicitely state that their own cause is equally justified and worth the sacrifice of their friends' lives and their own. They may think they praise friendship, but are in fact often tricked into praising their governments or military leaders. In the case of those Legionnaires in Vietnam, for example, the justification is highly questionable, as we all know. Not to mention the Nazis.

Also, the (possibly unrefusable) reasons for entering a war are often wrongfully transferred to specific actions, even war crimes.

Don't blame the song, but don't sing or play it, or other songs with similar messages.

I just read about Remembrance Day. Let us mourn the victims (innocent, friendly, or neither), be suspicious about justifications, and praise those acts of true heroism that resulted from self-determined valid moral motives.