Apple TV and Dish Network

In the last week, I just started having issues with both my Apple TV 3rd Gen and Apple TV 4K. Neither will connect to any input on either of my newer televsions unless I disconnect the HDMI cable connecting my Dish receivers from the televisions. If I disconnect the Dish Network HDMI cable, both Apple TV's function normally.

When both Dish Network and Apple TV HDMI's are connected, I get nothing. One television skips the input where I have the Apple TV connected, and returns to the Dish Network input. The other television just shows nothing on the input where Apple TV is connected.

This is what I have tried:

1. Unplugged Apple TV's.

2. Reset Apple TV's.

3. Replaced HDMI Cables.

4. Applied all software updates.

5. Read every forum online that I could find.

Any suggestions would be appreciated!!