I currently have a working MacTex 2014 installation and Homebrew installation on OS 10.10.3, and am about to install MacTex 2015. But I'm concerned about permission issues. Both packages install in /usr/local, and Homebrew requires very specific permissions on that directory to function.
Will installing MacTex 2015 change anything in my Homebrew installation? Will it in any way affect how Homebrew works?
No, MacTex installs to /usr/local/texlive, and installing it won't change permissions on /usr/local or any other subdirectories of /usr/local.