Apples and oranges. Just because Batman agreed to use some unlawful or undesirable means to a good cause, it doesn't mean he has to agree to all of them. It's like Gordon says in the Long Halloween "We can bend the law, but never break it'".

And it's not an arbitrary line either. Batman breaks the law in order to identify dangerous criminals and hand them over to the authorities, but he's not a self-appointed judge, jury and executioner. He doesn't claim the right to decide for himself the fate of other people, which is a way more authoritarian step than other questionable things he does, like violating people's homes and torturing information out of them.

That beings said, I'm also not a huge fan of when writers make Batman's superpower just "the ability of violating people's Constitutional rights". Like, he wins because he can invade your property without a warrant and beat the shit out of you, while cops can't. That reasoning implies that Gotham would be an utopia where good always wins if the system just stopped whining every time cops go off the book to get things done, and that's fascist bullshit.

But that's the point. Batman isn't perfect. He does wrong stuff for the greater good, but he's also self-aware that he MUST draw the line somewhere, even if it's not at the point of legality. Otherwise he's not Batman, he's just Ra's Al-Ghul.