I confirmed if you put your XR500/XR700 in "Router Mode" and add another router in "AP Mode", the My Phillips Hue Bridge will work fine, no disconnection.
I have experienced the issue with my Phillips Hue Bridge too when my Phillips Hue Bridge is connected to a LAN port of my XR700. My Phillips Hue Bridge won't turn on my lights when I'm pressing on button "On" in iOS/Android/Windows App. Sometime I have to turn it "Off" and turn it back "On" in the app, restart the App, or restart the XR700 so I can get back the connection between my bridge and the router.