Remove training CIs from external PR CI list. (#23425)
### Description
<!-- Describe your changes. -->
Don't exit if there's an error starting a CI. It's most likely an
intermittent error (or invalid CI) so it's better to keep going so you
only have to try and kick off the failed CI later.
### Motivation and Context
<!-- - Why is this change required? What problem does it solve?
- If it fixes an open issue, please link to the issue here. -->
Remove invalid CIs from list
