I have a new Git project in my Eclipse and the Staging View's Unstaged Changes panel shows not only the file I'm working on, but also
while these are set to be ignored in Eclipse's
Preferences > Team > Ignored Resources
This has nothing to do with Git or Git-related Eclipse views like Staging View's Unstaged Changes panel.
You would need to put those filenames into a .gitignore in order for them to not appear in that panel.
Then switch back to your Eclipse, and see if the Staging View's Unstaged Changes panel has still elements it should not display.
You can check if an untracked file is actually ignored with:
git check-ignore -v -- .classpath