Homebrew only supports one user (AFAIK). We had shared iMacs at work, and some stuff was installed using homebrew with the permissions modified so everyone could access what was installed. One night I got bored at work and upgraded some things... Which changed the permissions back to only the user that installed the cask (or whatever) and broke the terminal and other things for everyone else. My coworker was pissed the next time he saw me.
Any sane Linux package manager (I'm not counting Snap and FlatPak) installs stuff system-wide and all users can access the installed packages.
Linux is inherently a multi-user OS but Apple apparently stripped that feature from OS X.
Of course things are going to break if you take something that's meant to be installed per-user and open up one user's installation to everyone else on the system. Not Brew's fault your company's IT used it outside spec.