Well, looks like you are not in a position to change these policies. Therefore, if you regularly feel "a combination of frustration and shame working for them"

Well, looks like you are not in a position to change these policies. Therefore, if you regularly feel "a combination of frustration and shame working for them" rather than just a short period of negativeness / sadness that goes away quickly, it's not likely that it will get any better later and quite possibly worse. So quitting seems like the only option, doesn't it? I'd just add that regardless of your decision, try to take a step back and see if you could have spotted these issues earlier, before joining so that you'd be less likely to repeat this mistake in the future. Maybe there were some red flags that you missed or downplayed?