Thanks for the sample file.
Usually, it should not be an issue when printed if it looks correct in Acrobat.
To get it look right in other PDF viewers is sometimes a tedious matter. Exporting to a .pdf version that will flatten all transparency may often help, but then some of the non-standard PDF viewers may still display unwanted phantoms like ("white") hairlines or some other unexpected anomalies.
Based on your sample file, there may be a "fool-proof" way to prepare it for PDF viewers that cannot natively display complex transparencies: For example, put all type objects and path objects to separate layers, leave the raster images on one layer and rasterise that layer altogether. Then export to .pdf and check if it looks as desired in whatever PDF viewer you are using.