Is Buddhism a syncretic religion, and then what would they say on the Abrahamaic religions?

Original Buddhism is not syncretic.

The core Buddhism teachings (namely, the four noble truths, three characteristics, dependent origination, emptiness, six elements, here-&-now Nibbana with feeling, etc) are 100% original.

The Buddha is said to have said: "These were realities he had never heard about before".

This is the noble truth of the cessation of suffering’: thus, bhikkhus, in regard to things unheard before, there arose in me vision, knowledge, wisdom, true knowledge, and light. SN 56.11

If they were not 100% original, the whole idea of a 'Buddha' would be a falsehood since a Buddha is self-fully-enlightened without the help of a teacher (SN 6.2).

Buddhism (MN 115) states there can only be one Buddha in a world-system.

He understands: ‘It is impossible, it cannot happen that two Accomplished Ones, Fully Enlightened Ones, could arise contemporaneously in one world-system ― there is no such possibility.’ And he understands: ‘It is possible that one Accomplished One, a Fully Enlightened One, might arise in one world-system ― there is such a possibility.’

However, lots of modern Buddhism is syncretic. Theravada is 'Maha Vihara', which refers to a Hinduistic style Buddhism from Sri Lanka (which most of the posters on this chatsite believe in).

The less profound Mahayana Buddhist teachings are very syncretic, incorporating Hindu deities and esoteric Hindu & Chinese teachings about 'non-duality' and 'non-naming'.

Judaism is also very unique in its doctrine & does not appear syncretic.

However, Christianity certainty seems Syncretic, maybe the most syncretic.

Yet the Xtian fundamentalists believe it is the most original.

Buddhism is not a religion, it is a practice. Likewise, Taoism is a philosophy. ANd I would answer, no, it is not syncretic -- it stands on its own.

As to whether it's a religion, neither have any gods, so they can't properly be called a religion. Because even though they may be said to have scripture, these are not given by god, but by humans and so properly speaking could be said to be a perpetually-curated set of guidelines towards the perfection of the practice.

To the Asians, I believe they see it like a religion, in that they abide with a devotion by which only religion compares, yet that similarity doesn't make it a religion, in any Western sense, or even probably Near Eastern.

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.