Could one construct a cipher that is secure for friendly parties to use but insecure for hostile parties?
Mathematically, it can probably be done.  There has been research into trapdoor block ciphers.  See, e.g., A family of trapdoor ciphers by Rijmen and Preneel, and follow-up papers.

In practice, though, the problem statement is not realistic.  The assumptions are just not realistic.  Today, there's no reason why Red would be limited to using Blue's ciphers.  Instead, Red could just use any well-vetted cipher, like AES.  There's no reason why Blue should assume that Red will use Blue's ciphers; that's just not how adversaries are likely to behave given the current state of the public literature.  So while your problem statement might have been relevant and interesting to ponder 40 years ago, when there was no public literature on cryptography ... today, it is irrelevant.