A practical middle ground is: ask before making children’s photos public, and use limited-sharing by default.

The main point from the answers is that if you want to “show them to the world,” you should ask the parents first. That’s basic courtesy, and there may be reasons you don’t know about for avoiding public visibility.

For sharing with family, you don’t have to choose between fully public and fully locked down. Many photo services offer privacy levels such as private, friends/family, or unlisted/link-only albums. That lets relatives see the photos without exposing them broadly.

One workable system is:

• keep photos of your own children at a friends/family level;
• keep extended family children as family-only or link-only;
• use private or very restricted sharing for other people’s children;
• make event albums and share access links with the relevant family members.

If parents are comfortable with public sharing, you can still apply common sense about which photos are appropriate. But when in doubt, don’t post publicly without clear approval.