Homebrew is for Linux and macOS, allowing install of the latest compilers and other packages without sudo.

Use the Homebrew install script without sudo.

Install desired packages such as Gfortran:

brew install gcc

Generally the latest compilers are available from Homebrew for Linux and macOS.

Instead of putting Homebrew environment variables into ~/.profile, consider putting them into ~/brew.sh, where you can activate them when needed, instead of constantly being active. Either choice is fine of course.

Create ~/brew.sh containing:

PATH="/home/linuxbrew/.linuxbrew/bin:$PATH"
MANPATH="/home/linuxbrew/.linuxbrew/share/man:$MANPATH"
INFOPATH="/home/linuxbrew/.linuxbrew/share/info:$INFOPATH"
HOMEBREW_EDITOR="nano"

To use Homebrew, type

source ~/brew.sh

Upon closing the terminal, the configuration falls back to default (non-Homebrew)