I lived and worked in KS from 01/01-05/20/2020. I moved to MO on 08/01/2020 and work here. Why is my KS return also taxing my MO income when I lived in MO and not KS?

Where did you live (and work) between 5/20 and 8/1?

Technically Kansas is not taxing your Missouri income.  Rather, Kansas is using a prorate method to determine your Kansas tax.  In this method, Kansas pretends that all of your income is being taxed by Kansas and calculates what the tax would be on that income.  Then it determines what is the percentage of income that is taxable in Kansas, and then it multiplies the pretend amount by the percentage of income actually taxable to Kansas.  This would include any income you earned in Missouri while still living in Kansas.