How do I prevent nginx from auto-loading using homebrew?
The ‘stop’ verb to ‘brew services’ will stop the service from restarting automatically on boot having ‘unregistered it from launching at login (or boot)’ per the help text shown with ‘brew services’. The file you mention should be removed when you ‘stop’ the service.

You can check whether Homebrew believes the service is running or should run on startup with the ‘list’ verb.

$ brew services list
Name    Status  User Plist
nginx   started root /Library/LaunchDaemons/homebrew.mxcl.nginx.plist

$ ls /Library/LaunchDaemons/*nginx*
/Library/LaunchDaemons/homebrew.mxcl.nginx.plist

$ sudo brew services stop nginx
Stopping `nginx`... (might take a while)
==&gt; Successfully stopped `nginx` (label: homebrew.mxcl.nginx)

$ brew services list
Name    Status  User Plist
nginx   stopped      

$ ls /Library/LaunchDaemons/*nginx*
zsh: no matches found: /Library/LaunchDaemons/*nginx*