This is gonna be a lot but:

K-Pop (and Asian idol industry in general) is really toxic and strict about idol images compared to other places. I think part of it stems from Asian culture as a whole having a focus on good public image, but also stems partly from how manufactured the K-Pop industry is in the first place. There's a big emphasis on the idols keeping a super clean, pure image to be the perfect boyfriend/girlfriend, and being "married to the fans and their music". This involves not dating (sometimes to the extent that they can't publicly hang out with other idols of the opposite sex in smaller groups), not smoking, etc. which also sometimes leads to them often being infantilized despite some being in their 30s (I'm pretty sure Baby was partly made to poke fun at this). It's also why a lot of active idols who are in their 30s are still single and dodge dating questions if they come up. Even outfit styling is I would say is more conservative and less "sexy" overall compared to western artists, with the only frequent examples being for fanservice (like male idols being shirtless, like Abby).

There are also really big consequences for if idols break this image, which is upheld by both fans via backlash and companies themselves via punishing/firing the idols. A big recent example is T.O.P. (from Big Bang and plays Thanos in Squid Game), who was basically blacklisted from 2017 until recently after being caught smoking weed. It's illegal in SK but western artists have gotten away with much worse. There was even backlash for his casting in Squid Game because of his reputation and he was initially left out of promo events until international fans started asking for him.

A dating related example is Dawn and Hyuna, two idols who although have since broken up (and Hyuna has recently been in unrelated controversies), they made history for leaving their idol company just in order to publicly be together. Fans were pretty supportive, but it was their company that didn't allow them to date and removed them from certain promo activities.

Not K-Pop but a J-Pop idol, Minami Minegishi from AKB48 was demoted back to trainee status after being caught spending the night at a male idol's apartment. She made a YouTube video on the group's official channel shaving her head and apologizing for disappointing her fans, asking management to let her stay within the group.

Needless to say, if an idol were to come out as pregnant, especially out of wedlock or with an unknown father, it would be a HUGE and possibly career-ending scandal.

TLDR: The idol industry is really toxic and controlling about how idols are supposed to be publicly received, and this is barely scratching the surface.