Just some thoughts from an Outsider's perspective:
I don't know anything about Jae or Day6 but I watched some of the initial controversial video and this apology video out of curiosity. One thing I have to give the guy credit for is that this video doesn't seem like the pre-planned apology BS written by legal suites that you find in kpop. It seems genuine: Whatever he's saying is probably what he feels at the moment. Nobody would be struggling this much getting words out if they had planned to regurgitate some sort of apology script in their head.
And maybe some people don't know this but guys sometimes say dumb, racist, and sexist sh*t when we're around other guy friends but we don't really mean them or take them seriously. It's more like the absurdity of it is what we find hilarious. Basically, it's the same energy as a 10-year-old boy laughing hysterically at the word "boobie". Is it childish and immature? Sure. But tbh, there's a LOT of adults out there that still feel like kids inside just pretending to be adults. Lawyers, surgeons, business owners.....I've met many of these man-childs. Most of them though are still generally good people at heart.
But the thing is most of us know NOT to say these jokes in public or outside of our little male friend circles. Words can be harmless when they're not heard but can be harmful when they are. Jae's problem is that he was stupid and immature enough to forget this and say the joke in a public forum. He was probably in a head-space where he thought he was just hanging out and chatting with a couple of online buddies. There's really no excuse for his lack of awareness and stupidity, and lack of understanding about how certain words can hurt and damage others.
Now I've actually met truly misogynistic guys. Real scum that don't really see women as thinking, feeling people but more as just toys to take advantage of and play with. I don't really know this Jae guy personally but I just really don't get that kind of vibe coming from him from what I've seen. I'd say he's probably more just an idiot that needs to be more considerate and self-aware about things. He's probably redeemable.