Unitarianism did grow out of Congregationalism (which itself had grown out of Puritanism. How do you like your irony?). The evolution of Massachusetts religion is a very curious tale.
As to the OP, I believe one reason sex was either hedged about with taboos or altogether disapproved of by religions was that physical pleasure is so compelling and absorbing to the human soul. It can attract so much, that it is perceived (rightly or wrongly) as taking people’s attention away from devotion to God where it belongs.
(Sidebar: I once had a Hare Krsna friend, who was also a dope dealer… he had mental problems but was a nice guy part of the time… anyway, once he told me he had a new girlfriend and he hadn’t been to the Krsna Temple in a while. When I asked him why he didn’t go, he said, “You know, when you’re in bed with your girlfriend, and you say I’ve gotta go to the temple now, and she pulls you back into bed, saying, Oh come on honey, let’s go at it again … what can you do?” I think this explains why religious clerics are down on sex. They think it diverts human resources away from their projects.)
But I would like to present the Tantric point of view, which is the other side of the question, and doesn’t get equal air time.
In Tantric philosophy, sex and other pleasures do not necessarily take you away from God. They can, on the contrary, actually take you closer to God. If approached in the right spirit.
Pauline Christianity and some Hindu sects like Hare Krsna are almost totally against sex. They grudgingly admit that it’s necessary for reproduction, so the Church can get more followers. But when you do it, you should be careful not to enjoy it, just regard it as a distasteful duty for the Party (err… I mean the Church).
Judaism and Islam do not take that attitude. They positively encourage the sacredness of sexual pleasure, and so have a somewhat Tantric understanding of it. However, for sex to be sacred in Judaism and Islam, it has to be within marriage. So it it hedged about with limits.
Hinduism is not just one religion. It is an umbrella term covering many different cults, coming from different origins and often totally contradicting one another. The Vaishnava tendency within Hinduism is where you find the puritanical anti-sex attitudes such as in Hare Krsna (but oddly there was also a Vaishnava sex cult, documented in The Place of the Hidden Moon: Erotic Mysticism in the Vaisnava-Sahajiya Cult of Bengal by Edward C. Dimock and Wendy Doniger). This anti-sex puritanism in Hinduism is part and parcel of the patriarchal Aryan domination of India.
The pre-Aryan peoples of India had a Goddess religion of Shakti, which is where the Tantric sex-positive tendencies have flourished. It upholds the supremacy of the Divine Feminine, so woman’s body, the earth, and sex are all held to be sacred, worthy of veneration.