Does Hinduism acknowledge the existence of other religions?
No. Hinduism or more properly Sanathana Dharma predates mature religions which are well known today. Also, Hinduism evolved as a way of living or culture as opposed to a strict set of rules enforced by a religious/political/other influential body hence there is no need to compare or take examples from other religions.
The scriptures focus on stories (historical or folklore) to serve as examples for human living of what is right or wrong.There may be other old religions which do not refer any other. Religions that evolved much later, like the ones you mentioned draw inspiration from the Hindu or other older religions or were inclined to go against a certain set of cultural values based on their own beliefs and experiences, hence the mention or comparison.
While the scriptures don't mention any other religions, they also do not reject any form of worship and has several examples (Kannappa Nayanar) where standard practices are overridden and Bhakti (devotion) is highlighted instead. This is quite an unique and important aspect of Hinduism
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