Almost everything written down about pre-Christian Germanic religion was written by Christians, most of it centuries after conversion. The Poetic Edda and Snorri Sturluson's Prose Edda, the two central sources for Norse mythology, are thirteenth-century Icelandic works, produced more than two hundred years after Iceland accepted Christianity, by authors who were educated in Latin learning and who were writing partly to preserve the poetic craft the old material supported. Tacitus, writing in the first century, is earlier and describes peoples he never visited.
Anglo-Saxon and continental sources are mostly polemical or incidental. Against that, the comparative evidence of the branch itself is unusually valuable, because a divine name that appears in four Germanic languages is inherited rather than invented by one late author. The weekday names are the clearest case: Tiw, Woden, Thunor and Frig survive in English Tuesday through Friday, matching Norse Tyr, Odin, Thor and Frigg, and the correspondence is independent of any manuscript. That is why the branch matters here. The texts are late and mediated; the vocabulary is not, and where the two agree the ground is firm. Where they do not, the reconstruction cannot supply what the manuscripts leave out. A shared divine name says nothing about what was done for that god, by whom, or how often, and modern Heathenry has had to build practice out of a vocabulary and a handful of late descriptions. Its practitioners are generally clear about that, which is more than can be said for some of the scholarship they inherited.
Sources GermaniaPublius Cornelius Tacitus with The Poetic EddaAnonymous (Codex Regius), The Prose EddaSnorri Sturluson