There is zero chance of Starlink satellites interfering with Dish equipment, since the Starlink satellites transmit to the south, while Dish satellites are pointed north. The Dish Network dish reflectors on the ground are aimed to the south at the Geostationary location while Starlink points north. The signals are passing at near right angles to each other. If Dish’s reflectors can’t reject an off-center signal, then they’d be receiving other geostationary orbital locations.
Even if a Starlink satellite passes directly in the beam path from an Echostar GSO satellite to a customer’s ground station, Starlink’s small size and the speed it’s traveling means it wouldn’t block the signal for more than a microsecond and the FEC would handle the signal dropout.