Will my green card application through marriage be affected by bringing a different (renewed) passport to the interview than submitted with the form?

You should not have to redo the application. If the application is still at the National Visa Center, you should notify it of your new passport. If your application has already cleared the NVC and is at the embassy, you would do the same with the embassy. If the proper notifications are made and notations made in your immigrant file, there should be no adverse consequences.  Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.