The inks have changed. All are now safe. You can compost all paper.

Glossy kinds are often discouraged but the only "problem" is that the coating on the paper means that they will break down more slowly than will uncoated kinds.

Glossy paper has a high clay content that causes it to clump & be slow to decompose in the compost pile. Glossy paper & paper in general are best sent back into the recycling stream via curbside dumpster.

Some of those advertising fliers, with the glossy surfaces usually, will be printed with metallic inks which are then covered with lacquer to keep those inks from smearing. Hold the sheet at right angles to a light source and these lacquered areas will appear even more shiny, Those would not be good to add to your soil
Glossy paper is coated with clay, as is a lot of other printing paper although most newsprint is not, to aid in ink holdout. There is no good reason to not compost this paper even if your soil is clay. In a properly built up compost pile there should not be a problem composting even those clay coated papers.

thank you for clearing that up, I think I will just recycle the glossy ones and shred the normal ones.