A question I've never really been able to answer: do you feel it's morally permissible to like the shows everyone is mentioning (let's say fully understanding and opposing its problematic portions), or no?
Yes, it’s definitely okay!
It IS important to acknowledge and call out a show’s flaws. We should never be passive about things that are problematic. That doesn’t mean we have to give them up though, or that we can’t enjoy them.
Think of it this way: We all have people in our lives who we love whom are problematic. That doesn’t mean we should never talk to them again.
Now sometimes, there are people in our lives who cross a line. When that happens, it’s best to part ways with them. Other people cannot tell us where this line is. It’s something we have to decide for ourselves.