I haven't read the whole of Batman and the Outsiders #1, but I've seen scans of the pages where Batman claims to be unaware of a lesbian relationship among members of his team. Now this is Batman, the guy who is so psychopathically anal that he makes plans to defeat all of his friends and team-mates, on the off chance one of them goes bad. The idea that he would be unaware of a romantic relationship in a team he leads is laughable, unless you plan to do a plotline about him mellowing out or losing his grip.
Many fans have attempted to work out a rationale that enables this interpretation of the character to fit with how he has been generally characterised in recent years. It's something I've seen time and again where someone has acted completely out of character, or in extreme cases, appeared in one comic after they had died in another.
My advice is don't sweat it. Sometimes you just have to accept that the writer is a dick and let it go. It's not your problem that some writer has written a story that doesn't fit continuity, and it's not your job to fix it. The current run of Supergirl has contradicted itself so many times that most of her backstory up to the present issue is a pick and mix. Choose which parts you wish to believe and ignore what you don't. Don't try to make it all fit together because it doesn't.
Nobody can ruin Batman, or Superman, or Wonder Woman, or the JLA by writing them badly. These heroes will outlive any dumb characterisation, and if you want a rationale there will always be a Superdick Prime punching reality or a Mister Mind Chewing on the multiverse or whatever they hell they come up with next year to give them an excuse to disown all past mistakes. And with the afterlife having such a revolving door policy, it doesn't matter how dead a character is, they may come back one day.
So read the good stories and don't worry about the bad. Leave it those who are paid to do so try to make sense of it. Don't blame the character because the current writer is a lazy jerk with an agenda, and don't rescue him from his errors by attempting to rationalise them. It's not your job. It's his.