I have a 1998 chevy silverado pickup that is running great; no misses, no check engine light. However in the last few months if the engine is running, I am unable to use the garage door opening (hand held). I have two different manufactures of the openers (a liftmaster, and genie) both are circa 1998. They have worked well for years with the truck runnings. With the engine running, if I put the remote next to the opener it works fine.
The alternator was been disconnected and it is not the root cause of the problem.
If the battery in the remote is good, the next likely cause would be RFI from the ignition system. A minor discharge from the wires won’t make a noticeable effect on the running but will produce enough interference to effect the opener. Try opening the hood after dark and look for arcs.
The receiver is probably on the hairy edge of receiving anything and the car running adds to the noise floor. The receiver inside the garage likely has some sort of wire that serves as an antenna.
Try repositioning it so it isn’t next to metal, perhaps in a totally different direction to see if that makes a difference.
Try stopping in your driveway at about the place where you usually activate the opener. Turn off the engine of the truck and try the opener. If the door opens, then either the ignition system or the alternator is generating radio interference.
Interference with AM stations used to be a good way to tell your spark plug gap had gotten excessive and they were ready to be replaced. Along with the other suggestions, something easy to inspect. How long since you replaced them last?