Transparent redaction instead of white rectangle.

Here is a possible work-around that will semi-automate the chore:

Place your multi-page PDF into InDesign using the PlacemultipagePDF script included with InDesign.

Add a white box covering the unwanted elements, then move the box to the master page, which will apply to all of the pages.

Click through your pages until you come to a page with a colored background, edit the box color on that page to match the background color (override the master page first, to allow editing of the box color). Export to a new PDF.

If this PDF is just for printing, you are done.

If you need to permanently remove the covered elements, You can do this with PitStop using the Remove concealed objects tool. I don't think there is a comparable Acrobat tool, other than Redact, which I believe will rasterize everything.

What happens when you use the color of the colored pages?

Set the Properties of the Redaction tool to "Transparent Fill" and "No Tet" the red outline is to mark the items that will be redacted when the redaction is applied. This outline and apply redaction steps are done so one can check the selections being redacted prior to the actual action. The redaction boxes are a very special type of annotation and can be edited or deleted as needed prior to applying the redaction action. Once the redaction is applied there is no going back or undo feature. I would suggest that you make a backup copy o the document prior to making any changes so you have a copy of the original document.

There's no such option. You can use the Edit Text & Images tool instead of the Redaction tool, but it's not as secure.