Julia, 93 bytes

l->sort(l,by=x->findlast.(collect(x),"CcJOoSsUabDdefGghjLlnPpQqrTtuVvXxyABFHIiKkNRYZzEMmWw"))

works with Julia > 1.3

uses as input and output a list of the words

based on this answer by @Noodle9

Try it online!

Julia 1.0, (削除) 93 (削除ここまで) 92 bytes

l->sort(l,by=x->findlast.(i for i=x,"CcJOoSsUabDdefGghjLlnPpQqrTtuVvXxyABFHIiKkNRYZzEMmWw"))

Try it online!

works with Julia > 1.3

uses as input and output a list of the words

based on this answer by @Noodle9

edit: replace collect(x) with i for i=x (-1 byte)