Is it safe to remove the rings on jars for long-term storage of home-canned goods?
If the jars are properly sealed the vacuum in the jar and the waxed edge will hold the lid safely sealed. Undisturbed those jars will remain sealed until they are opened. The ring will reduce the risk of "unintentional" opening and that is really all the ring does. There are two real advantages to removing the ring once the seal is set. 


If something spoils in the jar it is likely to pop the lid open. Spoilage would give off gasses that would increase the pressure inside the jar and break the seal. This is more obvious if the ring has been removed. 
When it comes to juices, unintended fermentation is an issue. Even if raised to a temperature that is expected to kill yeast sometimes some of the little buggers get through and will ferment juices. Without the ring the fermentation breaks the seal. This prevents jars from exploding under pressure (yes, it can happen). I had a grandmother who would can grape juice, but did not want 'wine'. When the lids popped it identified the jars that had fermented, and which could be disposed (sometimes not the way grandma intended). 


I prefer to leave the rings on as when the jars get stacked up in the pantry jars can get jostled and a lid may get accidentally opened, but there is nothing "wrong" with taking them off.