It'd be awkward for one CW show to avoid the "soap opera" tactic of changing one's face (Batwoman) only for this to get away with it. There would be backlash to that for sure from the Kate fans
They're different shows with different storylines and different creative teams. They're also different categories of character, lead and supporting. It would be illogical to expect the same outcome from two such different situations. Each show's team should make the best decision for its show. Someone else's show is someone else's responsibility, not theirs.
IMO, some humor should be off limits if they are hurtful or offensive. For example, saying something racist is not bad if it is serious but totally ok if it is a joke. Racism should always be wrong. And I would hope that people would use common sense before making jokes. Yes, joking and humor can be good things but we should still think before we make a joke and ask ourselves if the joke is in good taste or not. For example, I would never make a joke about Hitler being a great guy, not even for shock value, because I understand how such a joke would be in very poor taste and very offensive.
You're quite right. It's illegitimate to say that hurtful comments are somehow not hurtful if the person who says them thinks they're funny. If someone thinks it's funny to cause someone else hurt or to demean them for their identity,
that is exactly what they are doing wrong, so it's bizarre to claim that somehow makes it okay.
When I was a kid in school, the bullies thought it was hilarious to torment me, to demean me, to make me feel hated and worthless and afraid. They thought it was a terrific joke. But I was traumatized for life. Thinking it's funny to be hurtful does not make it harmless.
Now, Sawyer has shown signs of understanding. He hasn't used "it was just a joke" as an excuse to say he didn't do anything wrong. He's accepted that it was wrong and harmful, he's apologized, and he literally said "Thank you for holding me accountable." So he understands why they let him go and he agrees with the decision. Still, the fact that he ever thought such jokes were okay to voice in public, where their targets could see them and be hurt by them, is not an easy thing to excuse. It's something he appears willing to work to redeem himself for, but part of redemption is accepting consequences and making amends. Lots of people before Sawyer have resigned from their jobs once inappropriate comments they made in the past have come to light. It's a way of doing penance, and the fact that he accepts it rather than resisting it is a good start.