Mining isn't essential to cryptocurrency - all that is needed is cryotographic verification. It may be heretical to their ethos but that doesn't disqualify it even if the goals vastly differ.
This limits its value as a currency. It's like the “7 degrees of seperation” thing. You might not be doing anything with librecoin that the governments of the world don't like, in the network of where the currency could flow would like to but can't it has a cascading effect which severely hampers the size the network can grow to.
For example, if you trade with John who trades with Alice who then tries to trade with Eve, but Eve doesn't want to use your currency becausesshe's doing something Facebook or the U.S. government doesn't like, then Alice won't want to use it because she can't trade with Eve, and then John will be turned off to it for the same reason all the way back to you.