Okay ik no one gaf about my yumeship but I wanna talk about this anyways because I think about it all the time.
Anthony and Bruce's relationship, though it is very loving and passionate, is fundamentally unhealthy because they actively enable each other's worst habits. They love each other, yes, and they make each other better people-- but at a core level there is definitely an argument to be made that they also make each other worse. They are a deeply, innately flawed partnership in the way that any relationship with Bruce kind of has to be.
I think it's pretty easy to understand that, ultimately, Bruce Wayne cannot be the best man he could be while also being Batman. Although Batman has done lots of good over the years, in the end the symbol exists because Bruce is incapable of moving past the death of his parents. He will always be the eight year old boy sitting between their corpses in crime alley, and he has spent his entire adult life attempting to stop two bullets that were shot decades ago. If Anthony really wanted to and really put in the effort, he has the potential to seriously help Bruce work through those issues and ultimately put down the cowl. He could, but he won't. He doesn't even think about it. And the reason for that is not because he doesn't love his husband, of course he does, but because Anthony literally cannot fathom that Batman could ever be anything other than the perfect source for good. He absolutely HATES when anyone criticizes Batman-- this is partially why his relationship with Stephanie, Helena, and sometimes Jason can be a little strained, because they're a lot more willing to say when Bruce is wrong than Anthony is. Anthony doesn't even process that Batman could be, on any level, a negative thing, for Bruce or for the people around him, and because of that he will never be the one to make Bruce work on himself and move on from vigilantism, no matter how good for him it might be.
On the other hand, the situation is similar in vice versa. Anthony is Nightingale because he is incapable of moving on from his own guilt around continuing the cycle of abuse as a teenager-- mainly against the girls his abusive boyfriend was cheating on him with. Bruce knows this completely. He is fully aware that Anthony is driven by guilt, and more specifically guilt that is perhaps misplaced because ultimately he was a sick child who needed help and was consistently failed. What happened was a tragedy, but at the end of the day Anthony's involvement was much more that of another victim than a perpetrator. However, Bruce will never be the one to help him work through that and move past the need for Nightingale-- partially because doing so would require him to confront his own demons and most likely face the music about discontinuing his own crusade, but also because he fervently believes that Nightingale is a remarkable source for good in Gotham and across the globe, and if Anthony Taylor has to pay the price so that Nightingale can be a hero, why is that such a bad thing? It's exactly what he does; Bruce Wayne has absolutely paid the price so that Batman can thrive over the years. It can be argued that most of the Batfamily can say that.
So, yes, Bruce and Anthony adore each other, but there is a sort of willful ignorance that has to exist between them in order for their relationship to work. They view each other as nearly infallible, and in doing so will make an active choice to refuse any semblance of questioning that may come along with what they do. To Anthony, Batman will always be a good thing-- for Gotham, for the world, and if you asked him he'd probably say for Bruce-- no matter what he does. Even in Batman's darkest, most genuinely questionable actions, Anthony has defended him tooth and nail without any hesitation. He literally believes that Batman can do no wrong. To Bruce, Nightingale is the same. They may make minor, short lived mistakes, but ultimately their mission is pure and because of that how could they possibly be wrong?
I think the only one who's really aware of this, though, is Alfred. He loves Anthony, of course he does, but he'll always mourn for another life where Bruce settled down with a civilian girl and eventually lost interest in the cape and cowl, where he saw the error of his philosophy and worked to better himself as a man in ways he can't do with Anthony. But Alfred knows that can't happen-- he knew that Bruce was too far gone for that fantasy to ever be real after the first year of his new career ended, and so he settles for Bruce to find happiness in someone who indulges his need to fight, even if it kills them both-- because at least now he dies with some semblance of happiness. It's the closest he'll ever get to the real thing.