When running a project built by maven with the following dependencies:
org.eclipse.persistence
Because I could not find an answer for this problem when only using a Tomcat and this thread is often linked with this problem, I am going to post my solution here:
Since the signature is in the MANIFEST.MF you can change the signatures in the .jar files using 7zip or WinRAR to open them or simply delete them from the META-INF files of both .jar's and then import the changed files to your IDE.
A useful thread for the Signature-Mismatch-Problem is this thread: Java SecurityException: signer information does not match