The most notable example is the proposal variously known as "virtual structs" or "inheritance", which had a brief prototype implementation in Rust (circa 2013) solely to support Servo's needs (specifically regarding representing the DOM), but which met a wall of opposition from the community. Such a feature is still likely to appear sometime in the future (after all, if Servo needs it, then it's likely that others do too), but the Rust developers are taking their time to explore solutions that integrate the most cleanly with the rest of the language.
That said, we do take their needs into account rather highly, just like any project with a large upstream user.
Just like we wouldn't want Rust to be useful for only compilers, "only compilers and web rendering engines" isn't much better.