I used the global configuration archetype to confirm that the issue is in the dependencies used by the git plugin. The configuration round trip tests in the global configuration archetype pass when I run them without the git plugin dependencies and they fail when I run them with the git plugin dependencies.
The Apache commons-validator that the git plugin is using as a convenience provider to check remote URL's requires commons-beanutils 1.9.4. When I include commons-beanutils 1.9.4 as a dependency in the global configuration archetype pom file, the configuration round trip test fails with the TypeError: Cannot call method "hasClassName" message. When I include commons-beanutils 1.9.3 without the commons-validator, the same tests pass.
Since the commons-validator is just a convenience, I'll remove the dependency from the git plugin and use other means to check git repository URL validity.
I assume
commons-beanutils 1.9.4 (released in August 2019) is not being used by anyone else in Jenkins core or plugins.
Removing commons-validator will be an improvement for the git plugin, since it will remove a transitive dependency on several other components.