There is a communication link between A/V components, known as CEC (Consumer Electronics Control). CEC should allow seamless integration of the components. For example, if a user turns ON a cable box or Blu-ray player, the TV and A/V system should select the correct input and route audio and video. Unfortunately, the CEC specifications are vague and each manufacturer has their own interpretation of which component should be in charge. When there is a disagreement such as you are experiencing, each manufacturer will claim “never seen this issue before, it’s the fault of ...”. If enough users complain about a specific issue one or the other manufacturer might issue a firmware change to address the  specific issue. Unfortunately, the other manufacturer might also issue a change and the two changes butt heads.

You may be able to deal with this issue by installing a CEC defeat in the HDMI connection between ARC and the TV. This will allow the TV and RING to work out their own deal and ignore ARC. Note that a side effect of this CEC defeat will be to disable CEC control of ARC’s Volume. You’ll need to configure the TV, cable box, and ARC to use IR Volume control for ARC. In most cases, once setup, this IR Volume control will be transparent to the user. I’m somewhat surprised that a Samsung sound bar works through all of this detail, but CEC interactions can be strange. Since I have such a low opinion of CEC, I would not be surprised if at some point in the future the current Samsung/RING integration will break and it will be the other guy’s fault.