Here's the breakdown:
Hard plastic, glass, and metal (and I'm pretty sure wood and ceramic) won't hurt anything, and can't be hurt (at least on a chemical level - glass can chink and metal can crush).
Pure silicone can be stored with pure silicone, but not silicone compounds like TPR silicone.
Toys of most other materials should be stored individually, without touching each other. A good, simple workaround is to just use ziplock baggies. I have heard that really old jelly toys might react to these, but generally they work just fine.