Methylene blue is a cationic dye (positive charge). It stains anionic targets like DNA and RNA, so it stains cell nuclei heavily. Eggshell is primarily calcium carbonate and would not stain. RBCs would stain if they are nucleated, as in birds, but not in non-nucleated RBCs of mammals.

When choosing the staining for your target always ask yourself a question what target I'm staining for is actually made from is it a protein? nucleic acid? a lipid? something else? Based on the chemical composition the answer "what staining should be used for it?" will come naturally from a bit of google search.