How can dividends from fidelity and vanguard not taxable to state be entered into turbotax?

When you enter your information into your federal return, the information flows from the federal return to the state return.   If you enter the codes correctly then the state software will follow the tax laws for your state in regard to whether those dividends and/or interest are taxable in your state.

Why are the dividends not taxable by the state.

The two usual reasons are that they are  (1) US government interest or (2) interest on obligations of your state. 

For (1), after entering your 1099-DIV, you will be asked if a portion of the dividends are US Government interest. Check that box. On the next screen, you'll be asked to enter the amount.

For (2),  the dividends will be in box 11 of the 1099-DIV (or box 8 of a 1099-INT). A few screens later, you will be asked to enter the state(s) that the income is attributable to and how much.  Those amounts will be excluded on the state return (technically they are excluded from the  add back of federally exempt dividends).