Is it okay to compost non-organic materials in an organic garden?

I eat organic foods whenever possible. I’m going to be making a vegetable garden that is pesticide-free and, therefore, organic. However, I do know that chemicals linger in non-organic produce (which is, of course, why I don’t buy it!). Will compost made from non-organic foods compromise the “organicity” of my garden and vegetables? How do you know? Thanks!

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