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Home device tries to connect directly to the Internet Service Provider, bypassing the router

I have a router ASUS RT-AC1200. Firmware is the latest: 3.0.0.4.380_10931-gfed566f.

It is connected to my Internet Service Provider (ISP). The router has a static MAC address, which I don’t change at all. Different clients are connected to the router via LAN cable.

My ISP has filtering logic, that provides internet connection by MAC address. So the internet connection is stuck to this MAC address. When the MAC address is changed, it means a new device tries to connect to the ISP, and the ISP disconnects it and blocks the internet.
So, from time to time, I’m getting issues, that my ISP disconnects me from the internet. It happens let’s say once per couple of months. I need to call them to ask them to reconnect me.

We figured out that, the reason for reconnecting was a connection from a different MAC address. Last time we checked the new MAC address, and it is my Sony Television MAC address. It’s connected via LAN cable to the router.

So, how it’s possible, that my internal network MAC address is exposed externally? How to disable that “feature” or fix the issue.