Firstly, the jQuery UI resources were not included in your JSFiddle; this is why the tabs were not working and showing all the content.
Secondly, the reason there appears to be a conflict between the two is that the click
event for the links inside the tabs is bubbling up to the #sidebar
container and triggering its slide toggle. To prevent this from happening use event.stopPropagation() like so:
$('#tabs a').on('click', function(e){
e.stopPropagation();
});
Here is the updated fiddle.
I hope this helps!