I believe XSLT 1 is still working in all major browsers today. Here's a simple HTML 5 example with two pages sharing a header template: https://gist.github.com/MarkTiedemann/0e6d36c337159a3e6d5072...
That may be a fairly specific use case though, and largely it still works great today. I've done a few side projects with XSLT and web components for interactivity, worked great.
Here we go, looks like its 17 years old now:
> The only combination that fails to render these entities correctly is Firefox/XSLT.
Which is one good reason not to adopt XSLT to implement HTML includes. You just don't know what snags you'll hit upon but you can be sure you'll be on your own.
> Bug 98168 (doe) Opened 24 years ago Updated 21 days ago
Well it does look like someone's still mulling over whether and how to fix it... 24 years later...