iPhone 7 has a known bug that causes cellular service to sometimes fail - so the phone no longer works as a phone. Took phone with this bug into Genius bar, and was told they'd repair it for free - if I also agreed to have them repair a teeny crack in the screen for $150. They would not fix the cellular issue without the screen repair. Any ways around this? Any way to get Apple to fix their bug for free?
As alluded to in the comments, many hardware repairs require removing the screen. If the screen is damaged (no matter how minor) there's a very high risk of it shattering during the repair process, and that is why Apple (and many others) won't do a repair unless you're also getting the screen replaced at the same time.
As for your question on how to get around this, the only other option is to get the screen replaced somewhere else, or to try replacing it yourself. Then, once the screen is okay, Apple will perform the other repair as per normal.
However, please note that not all screens are created equally and that the money you save on a non-genuine screen may not be worth it in the long run. I've seen many cases of iPhones and iPads with non-genuine screens work just fine for a couple of months and then start to glitch like crazy.