This depends on programming culture. For example, at Google, if you commit a CL to a shared library that breaks another team, they will tell you to roll it back and fix the callers first, and you will. It's doable but it slows you down. Doesn't matter whose fault it is; they're long gone anyway.

In other situations you don't have to listen, but if a popular library doesn't pay attention to backward compatibility then they'll end up in a situation where major customers keep using an older version of their library and nobody wants to upgrade. And unless you want to keep maintaining multiple versions, you want them to upgrade.