It is fact not Tznius to walk behind a woman. This is a famous and clear Gemorrah, and the Halachah. How exactly to apply it to holding a car door open I’m not sure.
As far as the Tzedakkah, if you wish to do the correct thing if this ever occurs to you, you should ask a Posek now, what to do. There are other issues, re Taharah between a man and woman touching via an object, that are more critical here than Tznius. You should ask a shailah