The Justice League and Batgirl both have J.K. Simmons as Commissioner Gordon. It's strange, but JK Simmons always seems to experience this. In fact, he explained how strange it was that he reprised a character for both Marvel and DC. To quote his interview with Den of Geek:
Furthermore, he answered whether Batgirl and Justice League share the same universe.
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Does Batgirl share the same universe as Justice League?
Batgirl and Justice League do not share a universe, but it sounds like DC recast him for a reason. A multiverse merging reason.
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Since Batman V Superman, DC has been playing with the idea of its multiverse. In the interview, he discussed the multiverse further as follows:
Has J.K. Simmons become the staple of the universes? No. However, DC may use him to keep some things the same in the multiverse.
