Since it’s characterized as a franchise tax, non-DC residents don’t necessarily get a credit for it on their resident state returns, for example Maryland residents get the credit on their state tax returns but Virginia residents do not.
The difference is strictly how the various state tax departments view the DC franchise tax. Maryland takes the “substance over form” approach and views it as an income tax and eligible for a credit. Conversely, Virginia takes an opposite “form over substance” approach, takes it at face value as a franchise tax and does not allow a credit for it on Virginia returns. So if you’re a Virginia resident with DC business interests, any DC franchise tax you pay is out of pocket – you are paying tax on the same income in both DC and Virginia.
Conversely, most Maryland residents get a credit for almost all the DC tax they might pay. DC residents don’t get a credit for franchise tax paid, but can deduct the amount of income taxed on DC franchise tax returns from their personal DC returns.