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It is most likely a resource issue. One Microphone, one camera can be used by one app at a time. If the presenter has Teams running first, then Teams has the microphone and the camera in use. In order for Ringcentral to do its meeting it needs to take control of the microphone and the camera so it puts Teams on hold.

If you have two microphones and cameras on one computer, then you could "assign" a specific pair of mic and camera to Teams and assign the other pair to RingCentral. The problem is that this may not work well because of IRQ issue and one or other may not work or be choppy.

Besides installing more hardware as in a second camera and microphone; the easiest solution is to start RingCentral on your presenters computer. Then on a second computer launch Teams. Then from the RingCentral computer remote desktop into the Teams computer. This will bring up the Teams computer as a window on the presenters RingCentral computer. That way there would be no conflict of which app will control the microphone and camera.