A show with Gestapo antiheroes could work. Not saying it would be made in this environment, but it could work.

Most givers are religious. Most giving is religious. Many of the top charities are religious.

Heh. It's definitely not supposed to be Catholic (architecture, vestments, Richard Lewis hair…).
Banco Ambrosiano collapsed in this year, during a papacy with an impressive anticommunist intelligence network of its own.

They don't want to stir up shit this way. This is Gaad's own thing/bluff.
They'd rather had continued working at apprehending and turning/convicting/trading the illegals than reshuffling the legals again.

A publicized diplomatic crisis that is answered by expelling Soviet diplomats.

No, but clearly they have an ideological contingency plan for the threat of their American children believing in what they're working against. (College funds.)