Some LED's effect radio signals, some more than others. Also the radio frequency has something to do with it, if put my radio on the table under the dining room LED can lights in the ceiling most stations are lost completely while a couple of other stations still come in ok. Just move the radio a few feet away so it's not directly under the LED's and all is well. The kitchen can lights are worse in that no radio stations come in and the only thing not affected by those lights seems to be the wireless router. I'm on the laptop in the kitchen right now with the lights on and no problems but if I want the radio on in here the lights get turned off.
I assume the radio signal interference is the problem with the garage door openers. The LED I have in my garage opener is only on after it gets the signal to open the door. Plus the garage opener has an external antenna that ends well away from the opener itself so when I pull into the garage and the LED is on, cause the door just opened, the remote still works and will close the door.