Solution
Make a .gitattributes file in your working directory and add the following line to it:
*.docx binary
Why not just set core.autocrlf=false ?
This is useful too. But configuring .docx as a binary format solves not only this problem, but also potential merge issues.
What is the origin of this problem?
From http://git-scm.com/docs/gitattributes , section "Marking files as binary". Note the italicized section.
Git usually guesses correctly whether a blob contains text or binary data by examining the beginning of the contents. However, sometimes you may want to override its decision, either because a blob contains binary data later in the file, or because the content, while technically composed of text characters, is opaque to a human reader.
.docx format is a zip folder containting xml and binary data, such as images.
Git treated your .docx as a text (and not binary) file and replaced endline characters. As Microsoft-developed format, .docx is probably using CRLF, which might have been replaced with LF in the remote repository. When you downloaded that file directly from remote, it still had LFs.
In a binary file Git never replaces endline chars, so even the files on remote repository will have proper CRLFs.
Applicable formats
This is applicable to any file format which is a zipped package with text and binary data. This includes: