Etymology: Middle English, of Scandinavian origin; akin to Old Norse mjukr gentle; akin to Welsh mwyth soft
Date: 13th century

ME meke (earlier meoc) < ON miukr, pliant, gentle < IE base *meug3, *meuk3, to slip, slippery, slimy > MUCK, L mucus, Gr myxa

I just don't see anything incompatible with these two statements of etymology.