I definitely don't think there's anything wrong with having characters be kidnapped or otherwise incapacitated and prompting a rescue mission from other characters. The main thing that can make the trope insidious is the persistent tendency for this to happen to female characters specifically, often the only female character in their respective casts, purely for the glory of the male characters who come to the rescue.
When male characters are captured or kidnapped, my impression is it's far more common for them to continue to be active characters: we cut to their point of view, see them trying to orchestrate their own escape or get information out of the villains or whatever. This is often a great way to give a look into the villains' lair, show the character dealing with a grim situation and trying to be resourceful in a different way than usual. By contrast, the archetypal damsel in distress is often either barely a character to begin with or is assumed to be completely passive, never seen again until the rescue (or else seen only in a helpless state, telling the villain the heroes will definitely come for her, or being held at knifepoint while the villain makes an ultimatum). Suddenly her role in the story isn't as a character anymore, but as an object to be recovered. This is unfortunate, and when it happens to established characters the audience likes, really disappointing: we wanted to see her kick ass in the finale, but instead she's just a victim who needs to be rescued. She doesn't get to do anything.
So I think the issue is twofold. First, it's probably more interesting, if a character is captured or otherwise in distress, to make them a bit more proactive and have them still do stuff, and it's worth considering whether you can do some of that if you're going to write this sort of situation. Secondly, it's worth thinking critically about which characters you pick for this sort of role. If it just feels weird to imagine your male characters being kidnapped and not being able to get out of it on their own, why don't you feel the same way about the female characters? And if the answer is that you picked the girl because she's the most vulnerable one, well... why is that? If you really need a noncharacter who exists purely to be a damsel providing motivation for your heroes, that's fine, but stop and think for a moment before automatically making it a girl just because that's the first thing that pops into your head. Main character's little sister? Well, why isn't it his little brother? Doesn't mean it can't be a sister, but try to make it a conscious, deliberate choice made for a reason rather than conforming to the stereotype just because that's where your brain goes first - that's where stereotypes do their most insidious work.
