We no longer have DISH, but I used both HMDI and the Red-Yellow-White plugs to the same television. And they both worked. Never tried them at the same time. Turns out, when I had Dish using the HMDI, my surround sound in the camper did not work. Sound only came from the television. When I switched over to the R-Y-W input, my surround sound worked through the radio-equalizer system. We used the R-Y-W input on that television more. Also, with R-Y-W, my outside speakers worked to. On HMDI, none of the speakers in the camper carried the sound.
So, to answer your question, both are active, and I imagine the coax connection is also active.
We quite DISH-TV by the way. Got tired of them constantly raising prices. Found out over-the-air satisfies our television preference just fine and doesn't cost anything, and no more haggling every time we had a bill increase.
