CJam, 34 33 bytes
ri{_2b,,2\f#_m*::|0+f^:mp:+!},2>p
Calculates all bitflip-resistant composites strictly less than n.
Like Jonathan Allan, I'm not sure if it's actually necessary to check for 0 bitflips. If it turns out that no prime number has all of its bitflips be composite numbers, the 0+ can be removed.