If there is a backdoor in an open-source system, and people know about it, then they will organize independently to patch it out. So it will be ineffective to the extent that the technology allows reprogrammability.

The only way you can beat it, as a governement trying to insert a backdoor, is through use of tivoization or some other technology that clinches control during manufacturing or other centralization weak points around economies of scale that the re-programmers don't have.