I haven't ever broken macOS doing stuff like that, and I've been doing it for years, with both Macports and Homebrew.

I use the default prefix and make sure the Homebrew stuff is in my $PATH before the built-in stuff and it works fine.

I understand things can break, but I have yet to run into such issues. Specifically, what exactly can break by replacing e.g. coreutils with GNU's?

What are you talking about? I've been using a similar homegrown setup for many years and never had any issues. In fact, I've come to appreciate being able to write directly on my Mac shell scripts destined to run on Linux boxen in production.