I have nontaxable combat pay. When I go through the IRS site, that site calculates I can receive the EIC if I exclude my combat pay. TurboTax wont give me the option.

Look at your W-2 box 12.  Does it have a code of Q with an amount?  This is your nontaxable combat pay.

Actually the non combat pay is not considered unless you opt to include it for the EIC & CTC credits not the other way around.   The program will automatically choose the better option for you.   This year you will have the option to enter the 2019 earned income & combat pay to potentially get bigger credits.   Follow the interview screens carefully in the Deductions & Credits section.