Is Buddhism a syncretic religion, and then what would they say on the Abrahamaic religions? Syncretism is a union or attempted fusion of different religions,
  cultures, or philosophies — like Halloween, which has both Christian
  and pagan roots, or the combination of Aristotelian philosophy with
  the belief system of the early punk rock practitioners.


I suppose some of my family are Christian, and though I wasn't really raised that way, I'm wondering, if Buddhism is syncretic, as with the Tao in China, how it has or will combine with the Abrahamaic religions.

Has there been any serious scholarship charting this, or even, though the idea seems off, predicting it?
It might appear that Buddhism is a syncretic religion because it apparently has some similar features to Hinduism and/or Jainism:


Rebirth
Concept of Karma
Samsara
Monks with orange robes and shaven heads
Beings like Brahma, Sakka / Indra, Yama, devas, gandhabba
Tendency to non-violence similar to Jainism
Some Mahayana deities resemble Hindu deities
The use of beads or rosaries in Mahayana Buddhism similar to Hindu
Tendency to non-violence similar to Jainism
Similar ritual elements like cremation and use of incense


In terms of philosophy, the oldest teachings of the Buddha are found in the Pali Canon, especially the Sutta and the Vinaya.

From there, we can see that some of the core and non-core Buddhist teachings, from the Pali Canon, are a stark departure from Hinduism and Jainism, and some are quite original:


The middle way between eternalism and annihilationism (both Hinduism and Jainism subscribe to eternalism of the self) - see this answer
The middle way between asceticism and indulgence (Jainism tends towards asceticism) - see this answer
The self is not eternal, not standalone and not independent - see this answer and contrast with Hindu BG2.24
The self or soul does not pervade the body (unlike the Hindu BG2.17) - see SN35.85
In terms of karma, not everything we experience is a result of past karma (compared to Jainism) - see this answer, SN36.21 and MN101
There is no Supreme Creator God (unlike Hinduism and the Abrahamic religions) - see this answer
The self or soul does not transmigrate (unlike Hindu BG2.22) - see this answer
Lay people eating meat that was bought dead and frozen from the supermarket is not sinful - see this answer


However, as also discussed in this answer, later on, Buddhist and Hindu philosophy influenced each other to produce Advaita Vedanta and Indian Mahayana Buddhist philosophy. Also, Tibetan Buddhism have adopted some Hindu deities. On the other hand, there has also been debates in later times between Hindu and Buddhist scholars (see this question).

However, Anatta and the lack of a Supreme Creator God, still keeps Buddhism very far apart from the other religions, and due to this, it is very unlikely that Buddhism will form a doctrinally syncretic relationship with Hinduism, Jainism or the Abrahamic religions. The syncretism is likely to remain at the cultural level, if it exists at all.