In my home directory I have files in a local git repository, because I want track them all under version control.
Most of these files I want to push to a remote repo
You can go ahead and actually track these files (sans the sensitive info), but then use:
git update-index --assume-unchanged
on each file. Then you can go ahead and add the sensitive info to each file, but Git will not see the file as changed, and not try to commit (and thus push) that sensitive info.
To get Git to update the info again, you'd use:
git update-index --no-assume-unchanged