Wiktionary says that the word "cross" (in English, and probably also German) was a borrowing from Latin that came with Christianity and had only the religious sense until about the 14th century, and then it started to replace the existing Germanic words for non-religion-related things that resembled crucifixes. Before that the words for things that crossed in Germanic languages were related to old English "thwart"/old German "quer" (from the same root as Latinate "torque" as in twisting). Whereas Latin crux goes back to the same root as Germanic "scharf"/"sharp". Which is super interesting and I would not have guessed!