It's sad, because the Americans I know do not conform to that stereotype, even the ones who are part of the religious right. Somehow, I think that to assert that such poor behaviour is typical of the religious is as erroneous as saying that it's typical of Americans.
Stereotyping is fine for creating a drama but it's a lousy way of judging a nation, or a belief system.
My understanding is that the more radical fundamentalists are indeed a minority, and that actually even many conservatives are not against say, gay marriage. The problem is that stereotypes of the family and ideal social order have been sold so thoroughly, for so long, in our politics that they still have this weight.
Someone screams "offensive" or "pervert" and "average" Americans (regardless of party) often remain silent or cringe. They may consciously be concerned about the simple cost of engaging the issue, or they may be afraid of explicit social stigma with the broad misconceptions still surrounding alternative social and private orders. By and large, people hold onto their few excused private pleasures (some would say "vices"). They don't want to look too closely at issues of sexuality and social structure. These things are considered muddy waters and the Reagan-Bush years have thickened the problem. Most people don't ask too many questions and risk appearing something other than liberated, happy adults who are cautious enough to keep sex "in the bedroom." They do not speak up to challenge the mythology that more conventional "family values" are the only known or acceptable standard.
Dealing with fundamentalist views of sex, family and reproduction is seen as a "special interest" matter, something more eccentric than environmental legislation (which has a wider following, but not a super effective one). That is left as something for a handful of educated, but still socially marginal gay activists to do... It's certainly far "below" financial crises and mismanaged wars. As a result, the effect of the fundamentalist conservatives is magnified. The usual political calculation is that addressing fundamentalism in the open here is both too politically expensive, as well as too low priority. The fundamentalists are often intimidating, persistent in their demands, relatively well organized/funded since at least the Reagan years, and they often threaten to upset action on other issues.
Partly cultural lag, perhaps? However, it is definitely related to increasing wealth disparities: The "private life" and often, rigid gender roles are advertised as the primary means of escapism - a tiny sample of one's true, "exotic" desires - in exchange for struggling with a weakened economy, lowered standard of living, and densely commodified life.
The same economic policies that have actually made it increasingly difficult
for the middle class to have something resembling a more "conventional," conservative family life (something of a stretch even in the 1950's) have made many people reluctant to expose home or "private" life to any debate at all. Yet, that is precisely the genre of debate that fundamentalists often call upon when they attempt to stir public scandals and to limit sex education, contraception or abortion. Unfortunately, for the most part, the fundamentalists are relatively more persistent about making an issue. They're liable to lose eventually, some thousands of undesired pregnancies and hundreds of hate murders of LGBT folk later... If they don't convince/inspire someone to start shooting and/or provoke riots in the name of one moral crusade or the other first. (Quite possibly even if they do, but I would rather not go there.)