What are your export settings?
The destination in the PDF preset under "output" is "Document CMYK: US Web Coated." There is another option to use "Working CMYK," though I'm not sure what the difference is between "Document" and "Working" for CMYK. Thanks so much!
The problem is, that you export a file to a CMYK output intend but your Transparency Blend Space is set to RGB.
BUT, I would strongly recommend not to place CMYK images in InDesign, place RGB images with valid profiles and convert them either upon PDF export as PDF/X-1a or even better, export as PDF/X-4 and let the Adobe PDF Print Engine (APPE) do the job to convert your images.
There is another option to use "Working CMYK," though I'm not sure what the difference is between "Document" and "Working" for CMYK.
The working CMYK is the one assigned by default in your color settings, but document CMYK may be different, and depending on your profile mismatch policies it may be preserved or converted to the workinig space when you open the file.
Did you check the file in ID with Overprint Preview on? Does it look correct?
Is your preflight setting set to find RGB?
If you open your PDF in Acrobat and go to Output Preview> Show> RGB, does that show you any RGB? perhaps in an effect?
As a test, export to PDF X-3, with Acrobat 5 compatibility, then look for RGB in Acrobat.
You might need to open and re-save an image in Photoshop that could be causing the problem.
Even if your PDF is intended to be printed as CMYK it is allowed with PDF/X-3 and X-4 to contain RGB images.
There is nothing wrong, if a PDF contains RGB files, depends only where the flattening is if it is allowed.
I have forgotten to mention: You shall place RGB images in InDesign files for print. They can be converted upon PDF export or even later which gives you a lot more flexiblity as if you would place CMYK files. It is a nonsense that RGB images are wrong if they are found in InDesign files.
Document CMYK is the assigned profile in Edit>Assign Profiles.... Working CMYK is Color Settings...>Working Spaces>CMYK. If there's no profile assigned, document and working are the same. So in this case Document CMYK is Coated FOGRA27 and Working CMYK is US Web Coated SWOP—the assigned FOGRA is color managing the document's native CMYK colors not the working US SWOP