Unable to activate wordpress importer after installing it

That error suggests that the WXR_Parser class is already “running” or declared. It’s possible that a theme or another plugin has incorporated that class and did not check if it existed already before initializing. ie. if ( ! class_exists( 'WXR_Parser' ) ).

To locate the source of the conflict, deactivate each theme and plugin one-by-one. You should be left with just a default theme active (ie. TwentyFifteen).