Upvote:4
A less than complete answer will be given if consideration is only given to the idea of non-Christian cultures adopting and invoking the number three from Christianity. After all, the number three is often used in the more ancient Hebrew scriptures, right from creation. This answer simply mentions two ancient, pre-Christian cultures that invoked the number three in their worship.
Although a triad is not a trinity, Hinduism has a triad of deities. The Hindu triad is called 'Trimurti' and is worshipped in the form of the guru principle Dattatrya. Let me quote from a Hindu scholar on this:
"Sometimes the three gods Brahma (a personification of the impersonal Brahman), Vishnu and Shiva are grouped together in a triad called Trimurti, occasionally although wrongly described as a 'Hindu trinity'." Encyclopedia of World Faiths, Ed. Bishop & Darton, p 193 article on Hinduism by Dr Ursula King (Macdonald Orbis 1987)
The ancient Greek goddess Hecate was also seen as a triad (which, again, is not a trinity but invokes the number three) The link I had for that, many years ago, is no longer working. Perhaps someone else can find one.
So, very ancient pagan religions felt the number three was highly significant in their view of their multiple deities.