Not sure if you still need a fix on this, but the problem is the plugin subscribes to the parse_request action, and in the function for it, attempts to remove itself. But the way that wordpress calls the list of registered actions is a for loop, so removing one while in the loop effectively skips the next one (and WP Router is likely registered on parse_request with a lower priority).
To the plugin author, I think you can just remove line 87 from restricted_site_access.php, unless you really need that line for some reason, in which case you might need to figure out a better solution:
remove_action( 'parse_request', array( $this, 'restrict_access' ), 1 ); // only need it the first time
For a quick fix without modifying the plugin, you can just add an action to be skipped:
add_action("parse_request", "fix_restricted_site_access", 2, 1);
function fix_restricted_site_access($wp) {}
This will be next in line after restricted site access and skipped, instead of the WP_Router hook.
