If I remember correctly from my digital communications courses in grad school bluetooth uses frequency hopping spread spectrum. Each of the bluetooth transmitters will most likely hopping around to different frequencies than all the others minimizing the amount of interference. Even if 2 transmitters happen to be transmitting at the same frequency for a short period of time there is probably some other mechanism to differentiate between both transmissions. These devices operate in the 2.4GHz frequency band so they already have to deal with all the signals from microwave ovens, wifi routers and other devices. I doubt multiple bluetooth devices would interfere with each other.

I personally have not run multiple bluetooth headsets near each other connected to different sources, but I have used multiple bluetooth deveices in close proximity (power meter, heart rate monitor, and headphones) and don't recall having any issues.

Bluetooth is master-slave, not peer-to-peer. In your scenario, the TVs are masters, the headphones are slaves. Every Bluetooth device has a unique spread spectrum modulation. When you pair a headphone to a TV, you might see more than one slave available to pair in the TV Bluetooth menu. If you only select one headphone, that TV won't broadcast to any other headphones. If you do that for every TV, pair it to a unique headphone, then there won't be any interference between paired sets. You can pair a master to up to 7 total slaves. Just be careful not to let more than one master (TV) pair to the same slave (headphone), then they both try to broadcast to that headphone and I'm not sure exactly what happens, but it won't be good.

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Brian

Gonna buy a fast car, put on my lead boots, take a long, long drive
I may end up spending all my money, but I'll still be alive

Should be fine. I work in an open plan office where typically there are at least half a dozen people using wireless BT headphones connected to their laptops or phones at any one time. Don't get any interference, and I can also walk out the door and 20 yards down the corridor to the kitchen without losing signal.

This. My work is the same, except we may have 40 people using BT headphones at one time, all within your signal range.

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You need will need to look for low latency blue tooth streaming device and low latency blue tooth headphones. If you use regular BT devices you are likely to have audio sync issues.

This would be a good place to start: https://www.amazon.com/...ow+latency+bluetooth

ROKUs do streaming audio through your phone or tablet if that is an option. I have this set up on bedroom TV and it's awesome. I don't have cable or OTA hooked up to that TV so that's not a problem.

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LLLEEEEEEEEEEEERRRROOOYYY JEEENNNNNKKKIIINNNNNS!!!

Agreed - annoying when the audio is behind the lips on screen. I have an older pair of Sony Bluetooth cans I use occasionally at night (to make the Mrs. happy) with just enough of a delay to be annoying, though it doesn't happen all the time.

But, some TVs actually have micro delay adjustments for audio (surprisingly to me) to match this up. At least my new LG OLED TV does, so I'm sure other high end models probably do as well.

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Fatigue is biochemical, not biomechanical.
- Andrew Coggan, PhD