In theory, it should be entirely safe (as defined in the OP's clarifying comment) to exclude the Findbugs transitive dependency. If used correctly, Findbugs should only be used when building the library, not using it. It's likely that someone forgot to add <scope>test</scope>
to the Findbugs dependency.
So - go ahead and try the exclusion. Run the application. Do you get classpath errors, application functionality related to the library that doesn't work, or see messages in the logs that seem to be due to not having Findbugs available? If the answer is yes I personally would rethink using this particular library in my application, and would try to find an alternative.
Also, congratulations on doing the classpath check up front! As a general practice, it is a great idea to do what you have done every time you include a library in your application: add the library, then check what other transitive dependencies it brings, and do any necessary classpath clean-up at the start. When I do this I find it makes my debugging sessions much shorter.