In my impression it is generally accepted that "red handed" referred to the blood-red evidence found on a thus discriminated criminal.
Then, what does "red handed war" mean?
New-York daily tribune. 1848 (2nd collumn, first line)
I sent you, to-night, a Telegraphic Dispatch, an-
nouncing the arrival in this City of a Treaty of
Peace. Yes, Peace, with angel fingers, has "fold-
ed the banner of red handed war".
Anti-slavery bugle.1846 (4th collumn, near top)
"If this church divides, it is but another
precursor of a division of the States and a red
handed civil war."
I searched only one variation in only one search engine, and found two of seven 19th century results showing this quite different sense. Naturally one has to ask where the phrase, and its parts, came from, but this can often not be determined precisely. It seems difficult to explain this sense derived from a set phrase "caught red handed" and thus unlikely to have been its original use and meaning.
I found it unlikely, though not impossible, actually even convincing, that "blood-" was the original sense. It's pretty hard to search for a term that is not precisely known, more so if taboo could be stipulated as the reason for its absence. So please forgive me if I didn't even try.
Its meaning is broader than murder or violence and could, today at least, describe a thief with pockets full of loot leaving the premisses through a window. This is more likely if no such forbidding sense as "murder" is inherently attached.
I rather suppose a link to rude (< Lat "rudis"), for several reasons. I'll spare you the details. I don't mean the question to be preoccupied, though I am.
Disclaimer: I'm not sure how broad is too broad for a question. Feel free to read and answer as narrow as you like. Not answering at all would be most narrow, implying there was no connection--that's not to say narrow-minded.
Suppose it matters, What is "red handed war"?
What's the oldest use of "red hand-"
Has it always implied blood? Does it, now? How was it coined?
Could it be a mondegreen, a reinterpretation within English? (if you answer to this, and not just not "Yes", but clearly "No" then you need a very strong reason; As strong as the requirement you would hold to an argument for a positive answer).
PS: After Tim Lyminton's answer I noticed mens rea and in medias res, "guilty mind" and "in the middle of the thing [deed, act, crime]". Of course, I can't establish a secure connection, neither with red, nor rew, and much less rude, nor G ruhe "quiet, still" so I will have to accept the given answer for now.