Not all Linux GUI apps run in WSL. Some of them are having compatibility issues especially when they depend on background running services (ex. dbus) or require security related features in Linux. Recent versions of Firefox and many other web browsers are having such compatibility issues.
Option 1 Wait for updates
Report your problems or share your findings with the developers of WSL and Firefox; let them fix the issues. Upcoming WSL2 also greatly improves compatibility and doesn't seem to have problems running Firefox or other web browsers.
Option 2 Find another web browser
Fortunately, Firefox ESR (Extended Support Release) seems to be compatible with the current WSL. You can download it directly from Firefox website. Firefox ESR doesn't support the latest features available in the current version of Firefox, but it has the latest security and stability fixes.
If you're using Ubuntu/WSL, Ubuntu Mozilla Team also maintains a PPA that can be added to your APT software repositories. The following outlines the procedure for installing Firefox ESR in Ubuntu:
sudo add-apt-repository ppa:mozillateam/ppa
sudo apt update
sudo apt install firefox-esr
Once a 'firefox-esr' package is installed, you can launch it simply by executing
Do you want to completely replace the original
firefox executable with
firefox-esr? You can execute the following commands:
sudo apt purge firefox
sudo ln -s /usr/bin/firefox-esr /usr/bin/firefox
You can now just execute
firefox for starting Firefox ESR.