The emboldening effect is well known when transparency is added to the page, and it often shows on screen in the PDF as well, and even in print from low-resolution devices.

Trnasparency can be "real" in the sense of an area of the illustration that has no background, or an applied blending mode, or an effect such as a drop shadow.

About all you can do is make things consistent by making sure there is something transparent on every page. You can do this by adding something to your master pages.

Since you can't prevent the effect if you need to use transparency in your layout, your options are to either live with bolder text on some pages, but not others, or to force it to look bold on all of the pages by makeing sure thay are all affected by transparency.

PDF/X-1a does two things that might not be desirable for you. First, it converts everything to CMYK, and if your destination is screen, that's not a good thing -- you'll wind up losing some of the brighter, more saturated colors from your RGB images that fall outside the CMYK gamut for the conversion space (wahtever that might be). Second, it flattens the transparency, if any is there. IN and of itself that's not a problem, but it can introduce artifacts called "stitching" the usually show as thin white lines surrounding areas of transparency on screen and in low-res prints. Like the emboldening, this is generally not a problem for hi-res press output.

Stitching can be eliminated on screen by turning off smoothing in the Acrobat or Reader prefs, but you can't control that on a user's machine.

I see my wording above wasn't necessarily crystal clear. Aside from applied "real" transparency (using the transparency slider), or areas of the illustration that have no fill so other stuff will show through when placed in ID, applied blending modes and effects are also "transparency" in terms of how ID behaves. Makes no difference if the effects are applied in Illustrator or ID -- a glow or a drop shadow is transparency in either case.