As America battles with a struggling economy and high unemployment, the Republican primaries continue to focus on the real threat to national wellbeing: the vagina. But first, let's talk about the hot new relationship that has birthed this B-movie, America Versus the Evil Vagina. Heck, it's the month of Valentine's Day and romance does seem to be in the air.

The participants in this relationship have, in truth, been circling each other shyly for some time, and it's not hard to see why: there are, increasingly, many similarities between the two. They could talk about their shared beliefs over a candlelit dinner, just like in Lady and the Tramp, but with more chat about the evil but simultaneously sacred nature of sex than who gets to have the last meatball. I am speaking, of course, about the Catholic church and the Republicans.

Now, the Catholic church has suffered a bad press of late. But when it comes to Catholicism I'm with Woody Allen's character Mickey in Hannah and Her Sisters: "It's a very beautiful religion. It's a strong religion. It's very well structured. I'm talking about the against school prayer, pro-abortion, anti-nuclear wing."

This strong and structured religion has found itself in clubby cahoots with the Republican party over contraception. Having struggled to gain significant ground in making it harder for women to have abortions, the representatives of both teams have decided to double down and make it harder for women to prevent pregnancies, full stop.

Last week, there were rising calls from Catholic leaders that religion-affiliated organisations should not have to provide health insurance that covers birth control for their employees as it is a violation of their beliefs. GOP candidates rapidly jumped on this bandwagon, some – like Rick Santorum – doubtless in wholehearted agreement given their belief that contraception is "harmful to women and society", others perhaps just seeing an easy means of bashing President Obama. Since Mitt Romney makes $600,000 a year investing in companies that manufacture the contraceptives he now seems to abhor, I'll leave it up to you to decide which camp he falls into.

In any case, Obama came up with a smart compromise: religious institutions won't have to pay for contraceptive coverage because insurance companies will provide it for free. This is because they realise that preventing pregnancy works out a lot cheaper than abortions and raising children. According to the Guttmacher Institute, the cost of birth control is a major factor in why poor women are three times more likely to have an accidental pregnancy than middle-class ones, and seeing as a major tenet of Christianity is to help the poor, and a major tenet of Republicanism is to get people off welfare, one might think they would support anything to prevent such occurrences. But no.

Catholic leaders and GOP politicians were so horrified by this move of Obama's that they have doubled down again (quadrupled down), insisting that all businesses should have the option to opt out of contraceptive coverage. Santorum has said that the compromise solution is an example of Obama trying to "impose his values" on America, which is something only Rick "I'll die to prevent gay marriage" Santorum is allowed to do. Newt Gingrich decreed this was proof that Obama is set to "wage war on the Catholic church".

Mainstream Catholics doubtless find it pretty trying that their religion is often reduced to little more than prurience and sexual deviance in the press. Similarly, old-school Republicans must be similarly baffled as to how their political party has gone from being conservative with a small "c" to "decidedly fringe". But this is what happens when, in the case of Catholicism, a group's leaders are so at odds with the flock: according to one study, 98% of sexually active Catholic women have used contraception.

As for the GOP, well, seeing as Santorum (who is a Roman Catholic) is leading the field, with 38% to Mitt Romney's 15%, one can't say that his views don't chime somewhere. But as Paul Krugman wrote in the New York Times this week, American conservatism's "divorce from rationality" stems from the party's long game of campaigning on racial and social divisions and ruling with tax cuts for the wealthy, only to end up with hardcore supporters who "believe in all the hokum".

In the case of both Catholicism and the GOP, those attempting to police what a woman can and can't do with her vagina are male. Several Republican female senators have broken ranks and voiced support of Obama's compromise. None of them, of course, are running for president. Far too liberal for the party nowadays.

So happy Valentine's Day, Catholicism and Republicanism. I have no doubt you'll get on grand. But perhaps the folk who would really relate to one another, and need a few drinks, are your disenfranchised supporters.

• The headline on this article was amended on 15 February 2012 to substitute Rebublicans for the original reference to the "GOP".