I cannot speak for other traditions but one of the pillars of Islamic religious thought and praxis, the hadith (reports about what Muhammad and his companions said and did) explicitly mentions the trimming of one's pubic hair.

For example, you have this hadith from one of the most important and well respected hadith collections, Sahih al-Bukhari:

(Isnad...)I heard the Prophet (ﷺ) saying. "Five practices are characteristics of the Fitra(purity, etc.): circumcision, shaving the pubic hair, cutting the moustaches short, clipping the nails, and depilating the hair of the armpits."

Sahih al-Bukhari, 5891  Book 77, Hadith 108

While we can debate how old the hadith are, and if they can be traced back to the time of Muhammad, this hadith (and several others on the trimming of pubic hair) was compiled by al-Bukhari (d.870 CE) and came to be accepted as a canonical source.

Most significantly, hadith (of which Bukhari was one of six canons) was one of the four sources of Islamic jurisprudence. Thus Islamic legal scholars deemed trimming one's pubic hair religiously sanctioned. We cannot comment with any certainty on the uptake of this practice across the Islamic world, but can probably say it was seen as a moral good from the 10th century onward.

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Sources

Joel Blecher, Said the Prophet of God: Hadith Commentary across a Millennium ( University of California Press, 2018)

Sahih al-Bukhari- Since it is still relevant to Muslim practice it can be found easily online

Debate on the dating of hadith: Wael Hallaq, The Authenticity of Prophetic Ḥadîth: A Pseudo-Problem Studia Islamica, No. 89 (1999), pp. 75-90.

On islamic law, Knut Vikør, Between God and the Sultan: A History of Islamic Law (Oxford University Press, 2005)