Everything looks normal using the commands you described, and it does appear to only affect status:
~/test (master)$ type git
git is hashed (/usr/local/bin/git)
~/test (master)$ git config --list
core.repositoryformatversion=0
core.filemode=true
core.bare=false
core.logallrefupdates=true
core.ignorecase=true
core.precomposeunicode=true
~/test (master)$ GIT_TRACE=1 git status -z
08:59:11.806197 git.c:348 trace: built-in: git 'status' '-z'
~/test (master)$ git log --oneline -1 -z | hexdump -C
00000000 35 31 35 39 30 65 30 20 49 6e 69 74 69 61 6c 20 |51590e0 Initial |
00000010 63 6f 6d 6d 69 74 2e 00 |commit..|
00000018
~/test (master)$ touch c d
~/test (master)$ git status -z | hexdump -C
00000000 3f 3f 20 63 3f 3f 20 64 |?? c?? d|
00000008
This is again with 2.4.3 from git-scm.com.
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