Objectively correct list on which Batfam members would swear
Bruce: no clue if he swears canonically or not outside of miller's all star b&r, but he should not. Look I am very opinionated on this. I do not think Bruce swears. Bruce values control over his own mind so much you know he would not want to do things that would make him look as if he is not in control of himself, even when he is not in control of himself. However, I do imagine that teenage bruce swore, as when Damian cusses Alfred out Alfred is like "Ah, memories" or something. Bruce was an angry teenager.
Damian: Canonically swears and would swear. him meeting the batfam by cussing out alfred is iconic i will not hear a word against it. he can be mean to people without swearing, too, of course. he just has a lot of tools in his arsenal.
babs: look, does Barbara canonically gamer-rage? Not really*. but she deserves it let her swear in anger when people are doing stupid stuff.
dick: I don't think dick is opposed to swearing on principal, but I don't think we have a lot of panels of him doing it in proportion to how long he has been in comics and not done it. I imagine it being more of in the "What the fuck" instances like when something weird or unexpected happens (and only when he's an adult or teenager, b/c as younger robin he was doing the 60s exclamations or whatever that everyone did)
stephanie brown: like dick I don't imagine her being opposed to swearing but I don't see her doing it a ton. I see her doing it more often in anger, since she's got quite a lot of anger locked up pre-Batgirl 2009 and possibly still in batgirl 2009
cass: cass isn't opposed to swearing, but given her propensity for mimicking the speech she sees around her in batgirl 2000, I don't think she'd do it a ton until she sees it on the videos she watches to figure out how 'normal people' talk. then she does do it, though I imagine it's less in anger and more just casually, since i headcanon that cass gets less verbal the more overwhelmed emotionally she is (which... IIRC is supported by canon? She stopped talking at some point in batgirl 2000 when she was on the outs with Bruce if I recall, it's been a bit since i did a read through)
duke: duke is another character I don't see as opposed to swearing, but I don't think he does it out loud on account of his mom clearly not liking it (at least he doesn't do it around his mom, or didn't back before she got joker-ified XD). he does in his internal monologue though sometimes
Tim: Tim canonically censors his own internal monologue IIRC in Robin 1993 you know he does not swear. possibly inspired by whatever cheesy 50s/60s exclamations his icon dick grayson made when he was robin.
*We do see her yelling and saying things she'd regret over comms, but also saying things you regret is like batfam 101 if you don't do it they kick you out.
