First of all, thank you for your service. We mean that. As the founder of RentJiffy, I know military service thanks to my father (Army, Korean War), my grandfather (Navy, WWII), and two uncles (Army, one WWII and the other Vietnam).
As a member of the Armed Forces, your State of Legal Residency (SLR) is considered your “domicile” or “resident” state from a tax standpoint as long as you are on active duty. Even if you are stationed in another state, you're still considered a resident of your SLR. So, you only file with your SLR and not any other state for personal income taxes. The same applies to your spouse if you are married.
So this begs the question, why does D.C. think you might need to file and pay taxes to them? The reason is that DC considers renting property a business function, not personal, regardless of how few or many rental properties you have and whether that property or properties are owned by one person, a few people, a trust, or a business entity. This is also why you had to obtain a business license to rent your property legally. Since it is considered a business function, all income derived from the rental property is considered business income, not personal. The federal law that shields active duty military members and their spouses from paying taxes on income to jurisdictions other than their SLR is for personal income only, not business income.
While you might pay your personal income taxes to your home state, business taxes can be levied by the jurisdiction where you are conducting business (in this case, D.C.), forcing you to pay taxes to that jurisdiction on the business income and this is why you would need to file the returns in D.C. and pay taxes.
RentJiffy’s thought: this arrangement where rental income is considered business income seems to be unique to D.C. We suspect this was intentional by design when the D.C. City Council implemented the law that included rental property as part of the business license categories in the late 1990s. You see, DC is one of the more transient places in the world. Almost 60% of residential homes are not primary residences, meaning most property owners are not D.C. residents. Thus, they would not report the rental income or pay taxes on that income to D.C. By making it a business activity, D.C. ensures they get the income taxes on the rental income from all owners.