Having two jars with the same class inside is not forbidden in Java, but is dangerous and that's why Android is being conservative and raising an error.
What could happen is that having two different versions of the class (say 1.0 and 1.1), when loading the class, one or the other gets loaded in no really predictable way. So, if the compiler let you call a given method on version 1.1, the JVM will not find that method cause it loaded version 1.0 which didn't have it. Replace method with everything else (constructor, field etc..), and consider that usually this happens with full packages and not single classes, so you'll have a lot of classes of version 1.1 not finding methods on other classes of version 1.0 and so on.
Java itself does not have a standard solution to this. However, jar files are nothing more than zip files, and unless they are signed they can be opened and modified and re-jarred.
You could open the closed source .jar, remove it's org/slf4j folder, re-jar it, and try if it works with the other version of org.slf4j.
Or better yet, tell those guys that having a "single jar" with every kind of stuff inside is not cooler than having the jars separated.