While this might sound random at first, I noticed that it
works in multiple languages:
Danish: brød (bread) = b + rød
German: Brot = b + rot
English: bread (spoken language) = b + red
Is this a coincidence?
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It is not a coincidence, but neither is there a link between the words - except that they consist of similar sequences of sounds.
The two words "bread" and "red" derive from Proto-Germanic *braudą and *raudaz. From these forms, the forms in the descendant languages can be derived by applying regular sound changes, and since the basic forms are similar, the resultant forms will be similar as well - because the sound changes treat the sequence *-aud- the same way, no matter if it's preceded by "b" or "br" (and, incidentally, these languages also preserve both "b" and "br" as such).
The same situation can be seen with other pairs of words that were similar in predecessor languages, like "bring" and "ring".
These similarities are because German, English and Danish (also Dutch, Frisian, Norwegian, Swedish, Icelandic, Faroese...) are Germanic languages, descended from a common ancestor (we call it "Proto-Germanic"). However, the exact meaning "bread" is somewhat of a coincidence, since the earlier meaning was something like "piece of food", so the Danish word might have ended up meaning "bit of cheese". "Red" seems to go back to an Indo-European word meaning "red". It is also a complete coincidence that "bread" in these languages contains all of the sounds of "red" plus something.
The party line would be that these words were similar in the common ancestor of those languages, and that the individual languages developed regularly, maintaining the resemblance. However, the etymology of "bread" isn't straight forward, whereas "red" is reconstructed for the hypothetic, ancestral proto-form of Indo-European languages, Proto-Indo-European (PIE) which includes non-germanic languages like Greek, Celtic, Latin, Sanskrit, Persian and a dozen others, which lack a closely similar word for bread.
The etymology of the noun is given as "Disputed". They tentatively link PIE *bʰrewh₁- ("to boil, to brew"). From the stem they derive *bʰrowh₁-tó- (with vocalism alternation and result-noun forming suffix), that could possibly give Germanic *braudą ("bread");. They further derive the stem from PIE *bʰer-, there glossed "to boil", but on the corresponding page it is glossed "to bear, carry", where they derive also e.g. Sanskr. भर्मन् (bhárman; "support, maintenance, nourishment, care") and many more words, often diverging wildly in meaning, e.g. "Slavic: *berďa (“pregnant”)". We already saw, those pages aren't fully congruent, and sadly that somewhat reflects the state of the art.
So far the party-line. However there is no etymology--at least none accepted--given for *h₁rewdʰ-. So the answer to your question could be: maybe.
Now for my open-ended interpretation, I would probably take a weekend. Consider brahman, phago-, ferment, break, blood, flower, to raise [a child; dough], German Wegzehrung, the prefix be-, the roots around rect-, rex, right etc., German bereiten, vorbereiten, zubereiten ("prepare") Proviant ("provisions, rations"), etwas gebacken kriegen (coloquial "to get something done*), En. to back someone ... Ger. auf die Reihe kriegen, etwas klappt, kleben, zusammen-backen, pappen, das Becken, En. bacon, big, bug, bud, bow, Ger. Bug, Bauch, PIE *bhew- ("to swell"; *bu-), Ger. Brett, Bürde, En. burden, broad, bristle, brush, Ger. Bursche, Geburt, En. berry, Ger. Berg, Brocken, Brücke, überbrücken, En. bridge, bright, Ger. Bereich. And that's only Germanic b and nothing to say of p or f or ... but a little bit of r: rühren, Rührteig, berühren, regen, rücken, Rücken, En. to reach [maturity] vs to be green behind the ears ("immature").
Certainly, bread turns brown if baked and there is something about color terms having had a wider meaning than today. A root for brown in PIE is reconstructed, but only on the basis of Germanic and geographically close languages, as far as I know. Also note that blood bakes or rather cakes in figurative speech, and that traditionally gory crusted blood was labeled differently from vital, flowing blood. Also note that in Japan, the sun is drawn red, as far as rising (or rather setting [of the dough?]) is concerned.
I'm not sure whether the difficulty noted at wiktionary lies in irregular sound correspondence or just the semantic shift and lack of cognates (there are likely scholarly papers on the matter to be found for the interested reader). Even in Old English "hlaifan", German "Laib" [of bread, cheese, the body] were mainly used to denote bread, but that's probably a different can of worms and that's nothing to say of our daily bread and the like.
By the way, if only for analogy, note that "bride" is likewise of rather uncertain origin (which Anatoly treated last year in the blog linked above, too).
PS: Funny enough, if we look at Ger. "Bereich" (realm, area) and compare area, we find the suggestion to look at another root that means "to burn", *h₂eHs-. I really wonder where the r should come from. But I'm done for today.
The phenomenon you just rediscovered is termed "exceptionlessness of sound laws": Words that have some common sound structure in a proto-language (here Proto-Germanic) tend to keep that commonness while undergoing some sound shifts (here final d -> t in High German, some parallel shifts of the vowels).
Of course, the complete lack of exceptions is kind of a dogma (but a very useful one in historical linguistics), exceptions occur in practice (e.g., because of subtle differences causing different evolution in the daughter languages or cross-borrowing). However, any postulated exception to a sound law needs a sound explanation to be believed by the community.