I think it's good for Christians to be aware of the many religious influences in Western Culture which are not Christian. It's good for us to to know these influences so we don't accidentally glorify or lift up false religions. It's also good for us to know to use as a starting point of conversation with friends when a religiously influenced song or movie is playing. It's simple to say, "Hey did you know that this song is talking about ______." It would then be a good opportunity to explain why Christians disagree with that belief and segue into what the Bible teaches on the issue.
I've been writing about Hinduism lately, while trying to make connections from those Hindu beliefs and practices to presenting the Gospel of Christ, using Hinduism as a starting point to springboard to a presentation of who Jesus is and what Jesus has done for us. While I write these blog posts, I'll also intermingle them with examples of how Hinduism has had influence in Western culture.
One aspect of how Hinduism has influenced the West is through the Beetles! The Beetles introduced Hindu instruments, such as the sitar, to the West. Influence of Hinduism can be clearly seen in George Harrison's song, "My Sweet Lord." The song initially sounds like it could be a Christian or Jewish song, singing about wanting to see, touch, and know the Lord, with "Hallelujah" being sung in the background. Later in the song, a shift is made to the background singers chanting, "Hare Krishna, Hare Krishna, Krishna Krishna, Hare, Hare, Hare Rama, Hare Rama" and etc. Krishna and Rama are both incarnations of the Hindu god Vishnu. Krishna is the most known incarnation of Vishnu. He is the central figure in the Hindu epic, the Bhagavad Gita, and in this epic he teaches that living out one's natural position and calling in life as an act of worship to the Lord is a way of reaching perfection. During concerts, Harrison would prompt the crowd to sing "Hare Krishna"!
I've heard that there were some Christian churches in America who didn't know the Hindu influence within "My Sweet Lord" and used it during worship services! So it certainly can be good to be aware of what other religions are saying, doing, and teaching, especially if the lines get to be blurry between what is Christian and what is not.