InDesign Export to PDF prints white box lines

If they are hairlines caused by anti aliasing they normally will not print. Ofcourse you want to check that. If you turn off  "smooth images", "Smooth graphics" and "enhance thin lines" in Page view in Acrobat you will disable anitaliasing and your lines should dissapear (the page may be sligtly more pixelated but since device pixels are at a higher resolution this will not be a problem in print).

Only use spot colours if your printer has a propper RIP or you are planning to print in spot colours. 

When they are printing at a customer a PDFx4 would be better as @Willi Adelberger  says. Though you say you have tried using PDF/x4? Also you need to confirm how they are printing (getting the PDF correct i only half way). For best results print from Acrobat Pro. If need be there is in Acrobat a Advanced setting to Print as Image. 

So to help you further we/you need to figure out when this happens. For this we would need to more about the design and more about the printer and that you confirm that you are printing from Acrobat and no other PDF reader. 
It is more common if you have designs with transparency. If possible put text above transparent objects (including PNG or Photoshop with transparency). Use the transparency flattener to find risk zones in your design. (https://helpx.adobe.com/indesign/using/flattening-transparent-artwork.html)

You have to asure that you only import PDF/X-4 in InDesign. This allows you to export to asll kinde of PDFs. But only with PDF/X-4 export you will eliminate stitching lines.

Acrobat 4 compatibility will always give you stitching artifacts. Anything above that should retain transparency. You'll have to provide screenshots and better details about what "prints with white lines all over the place" means.

in the future, to find the best place to post your message, use the list here, https://community.adobe.com/

p.s. i don't think the adobe website, and forums in particular, are easy to navigate, so don't spend a lot of time searching that forum list. do your best and we'll move the post (like this one has already been moved) if it helps you get responses.

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