Updated for filing 2021 tax returns.
While you don't have to report your nontaxable pay as a member of the Armed Forces, nontaxable combat pay can count towards earned income for the Earned Income Tax Credit (EITC or EIC).
Counting your nontaxable combat pay as earned income still doesn't make combat pay taxable, and getting the EIC could reduce the tax you owe (or boost your refund).
That said, it could also reduce the amount of the EIC you get if you have other earned income, too. The EIC requires that you have some earned income to qualify, but the more income you report, the less of the tax credit you qualify for (because the EIC is designed to help low- to moderate-income taxpayers).
Plus, you can't just use part of your pay towards the EIC; if you count any combat pay towards earned income, all of it has to be included. (If both spouses have nontaxable combat pay, each spouse gets to choose whether they will count their nontaxable combat pay as earned income.)
You definitely want to compare the outcomes of including or not including your nontaxable combat pay as earned income, just to see which is most beneficial to your tax return. That's a breeze when you file with 1040.com. It's easy to try both ways to find out which is best for you!
Note: Service members on extended active duty outside the U.S. are considered to live in the U.S., so they meet the EIC's residence requirement.