Building off of what Dfense said, there was also a huge difference between what the Scripture said in Christianity and what was actually practiced. While St. Augustine was highly anti-sex, and helped create an association between Satan and physical lust, this is less clear in practice. (I don't have a source for this, but I do wonder if part of that is trying to establish Roman fauns as demonic to aid the conversion process in Late Antiquity).

Until Sylvester II and, later, Gregory VII, it was pretty common for the Pope to have a concubine. Part of the Gregorian reforms were to ensure that more devout people (and therefore people that would support papal authority) were anointed as bishops. So, then it became less common for a while, then it re-emerged in the late Middle Ages and the Early Modern Period.

Similarly, there are a lot of folk traditions and poems that are pretty obviously sexual. the so-called "Key" riddle from the Exeter Book (an Anglo-Saxon compilation) sounds a LOT like the answer should be "penis." Similarly, May Day/Walpurgisnacht rituals are rather clearly fertility-related and were at least tolerated in the Christian Church.

Finally, looking at literary production, there is a lot throughout the medieval period that celebrates sex. Many of the romans genre celebrate both "pure" and carnal love, and were extensively copied both by lay people and monasteries. Chaucer and Gwerful Mechain were definitely Christian, and also wrote highly explicit poems. And, visual art, such as Paris, Bibliothèque nationale de France, MS. Fr. 25526, f. 106v (which depicts a nun picking penises off a tree), suggests that there was a lot more openness to sex in the Christian world than a reading of Scripture would suggest.

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So, in sum, I don't think it's a block difference between Christianity and non-Abrahamic religions (I do not study Jewish history at all, and I know only some Islamic). Certainly, at some times, Christianity is diametrically opposed to sex; however, the phenomenology of medieval Christianity, at least, appears to have been far more open to sex than the doctrine was.

You're right that non-Christian religions (both before and after Christianity) often either accept that sex is a part of the natural world or celebrate sex as an important religious symbol or practice. The pairing of two genders, the yin mixing with the yang, male with female, fertility and the magic of the creation of new life, regrowth, cycles... They're all very important to many non-Christian belief systems.

There are also quite a lot of sexual... events, shall we say, in the Old Testament which would not fit the hard anti-sex sentiments of many Christian churches. (One such example is Genesis 19:30-38, where Lot's two daughters decide to get him drunk and have sex with him to impregnate themselves since there's nobody else around to have sex with, and their father deserves to have sons. Lot is considered a righteous man of God.) See the Song of Solomon for an Old Testament celebration of love and lovemaking.

Important changes were made for the New Testament, which is far more judgmental about sexual matters. Considering the context of when and where the New Testament was written (sometime between the life of Jesus and 400 CE), one might surmise that the perceived sexual excesses of the pagan Roman Empire may have been targeted and denounced by the early Christians as a way to delegitimize their civil, political, and religious opponents. I am not an expert on Rome, however, so I'll leave the more detailed and certain accounts of this to others.

I will lay a significant portion of the blame on Augustine of Hippo's door (Saint Augustine) due to the strong anti-sex influence he had on the Catholic church.