Just use job with trigger as parent job to start your pipeline (like a separate job which just calls child job). The way it works that GitHub trigger scans all SCMs and listens on all of them.

I'm not sure I follow. The issue is that pushing to a git repo that is never checked out using GitScm in a pipeline and is used only as a global pipeline library should not trigger builds.

Other jobs that are are not pipeline jobs but use git push triggers do not have this issue.

Probably pipeline adds this type of scm like regular scm. So my suggestion is to split trigger and pipeline to different jobs

I see what you're saying. This still feels like a bug with the github plugin since it's the one responsible for registering GitHub hooks, no?

This means I have to have a trigger job for every pipeline job, right? 

Will setting poll: false remove other other git repos from being triggers as well?

These are very similar. One is a globally included library and the other is a locally included librar.

Even worse, builds are triggered if unbuilt changes are pushed (and a job unbuilt) and a commit on a different branch is pushed to the testing repo.