The duplicate candidate shows it in Affinity Designer and Photoshop. Here's a receipe for Illustrator. I believe the gradients are the actual problem.
Make a gradient and add some grainy effect (Grain, Mezzotint, Pointillize) to it. Place the grainified gradient onto a shape with solid fill. Have a blending mode other than normal for mixing. Normal can be used with reduced opacity
White to black gradient has got effect Pointillize. It's placed onto solid color shape with blending mode soft light. Try other blendings, too and change gradient colors and opacity.
If you do not need gradient, have a solid gray shape, apply to it some grainy effect and place the result onto a colored shape. Use blending mode soft light for mild effect.
Warning: Grainy effects are complex to calculate. Having big grainified shapes can make Illustrator slow when you make edits. Expanding the appearance of the effected shapes (=Object > Expand Appearance) helps, but the shapes are changed to bitmap images. Have also hidden copies of non-expanded shapes to be able to make scalings or other edits in vector domain.