Is it safe to compost cereal type boxes?

I made a post about a shredder being my new favorite garden tool.  Now I have been searching info on what I should and should not use in my compost.  I cool compost.  I never had any luck with hot composting, and have discovered its better for the environment not to hot compost, so for once my failure is actually a win.   Just so you understand where I'm coming from, I am the type person who removed the tea from the bag because I discovered the bag was made with micro plastic. Now I have taken it a step further and I drink loose leaf tea.  No bag to worry about.  My point is I make compost to add super nutrition and as little toxins as possible.(I would love to say no toxins, but that is just unrealistic.)  Now I'm wondering if it's safe to shred things like cereal boxes.  Everything I have read is contradictory.  My understanding is I would have to look up the contents of each individual box/paper product.  I would have to get an ingredient list and then understand the ingredients, which honestly I'm sure I won't.  I think I will stick to corrugated boxes (shipping boxes like what amazon comes in) and brown paper.  Maybe shred and recycle mail, and fold the other type boxes up so they don't take up a lot of room and rash them.  My original plan was to shred it all and put it in my compost and my vermicompost.  But with micro plastic, wax, and toxic chemicals in the dye and ink, well I think not.  Even though I think I have my plan of action I wanted to ask the amazing people of permies what you think, what you do.  Thank you very much.

If they have printing on the outside, I wouldn't. Something is keeping the printing from coming off, and I imagine it's some sort of thin plastic film. I put those in the recycling (here they actually do get recycled) and use the normal brown corrugated cardboard in my garden if I need to.

(I hear you on being flexible.I take our old office paper and shred it for rabbit bedding, and when it's nasty it goes in the garden as mulch. It's probably not ideal, but I figure it's better than the other options, like buying some other thing that was specifically made for the purpose)