the mixer output is male XLR, and my DI XLR inputs are also male. So I would need a female to female XLR to make that work.
This sounds like there might be a little confusion with the use of the DI box as well. Generally the male XLR on the DI box will be OUTPUT to the mixer. You would not normally use that connection as the input, especially on an active DI. The output from that male XLR would then go to a mic level female XLR on your mixer, not a line level input. The general purpose for most DI boxes is to take a variety of input signal types and convert them to a level appropriate for a microphone input at the mixer.
I am sure more experienced people can enumerate a variety of exceptions but my guess is your use of the DI box would be the "normal" way I have described.