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It would appear that the issue only occurs while the Bluetooth is actively seeking remotes to synchronize. This issue doesn't appear to happen in the OS because you have to manually begin the pairing process from the computer. During this time AirPort appears to be unable to communicate, however after that it works fine because it is no longer actively seeking new remotes. This is the reason that using a Bluetooth keyboard and mouse does not present the same problem as using Remote Buddy. Remote Buddy is ALWAYS looking for new devices, rather than only when you tell it to do so. You can turn this feature off, but then you cannot pair your device at all.
That being said, would it be possible to add a feature to Remote Buddy that causes it to look for a remote when it first comes on for a minute or two, and then require a key press, or a menu selection to re-trigger the search process? This should eliminate the interference once pairing has completed, and would only minimally increase the difficulty of connecting a new remote.
As for changing wireless settings, I have been unable, as of yet, to find any settings that allow AirPort and Remote Buddy to co-exist, therefore the only solution I can see, once a remote is paired or shortly after startup, is for Remote Buddy to stop looking.
