It's a long-standing puzzle to me that it seems so much clearer to me than to many other people that one of the basic drivers of the right-wing program is sexual hysteria. "Anti-abortion"ists want to punish sexually active women. Homosexuality is so deeply provocative that it can't be talked about rationally at all.

But I just ran into another angle, which hadn't occurred to me before, on the wonderful blog Mind Hacks —

Tell me about your mother superior

I found this fascinating aside in a 1969 article on 'Psychiatric Illness in the Clergy' about a group of monks who underwent psychoanalysis, causing two thirds of them to realise they were "called to married life".
The Pope immediately banned psychoanalysis from the priesthood as a result:

[Bovet] suggests that many clergy would benefit from psychotherapy during their training. This was attempted in Mexico when in 1961 a group of 60 Benedictine monks underwent group and individual psychoanalysis. However, of the original 60 monks taking part in this experiment, only 20 are still monks ; and of the 40 who have left the monastery it is reported that "there are some who realized that they were really called to married life" (Lemercier, 1965).
The Papal Court answered this "threat" the following decree: "You will not maintain in public or in private psychoanalytical theory or practice, under threat of suspension as a priest, and you are rigorously forbidden under threat of destitution to suggest to candidates for the monastery that they should undergo psychoanalysis" (Singleton, 1967).

This was not be the last time psychotherapists cause stirrings in the faithful.
The book Lesbian Nuns, Breaking Silence contains a chapter by the former Sister Mary Benjamin of the Immaculate Heart of Mary convent in California.
Psychotherapists Carl Rogers and William Coulson arranged for the nuns to take part in encounter group, essentially a form of fashionable 60s group psychotherapy aimed as well people rather than patients for 'personal growth'.
The effect was disastrous for the convent, with hundreds of the nuns defaulting on their vows, and several, including Sister Mary Benjamin, discovering repressed lesbian desires.
The convent eventually collapsed and was closed in 1970.
There's an brief online article that also recounts this story and I was intrigued to see a footnote at the end:

Having abandoned his once lucrative career, Dr. William Coulson now lectures to Catholic and Protestant groups on the dangers of psychotherapy, with a particular emphasis upon the "encounter group" dynamic.

There's a whole novel right there in that footnote.

Link to summary of 'Psychiatric Illness in the Clergy'.
Link to online article about Dr William Coulson.