In terms of deity worship, practices, and traditions. Other ancient religions seem to have spread somewhat widely like with the Greek pantheon, mesopotamian beliefs, and levantine theisms like judaism. Although these seem to be spread through nomadic wandering, warfare, and quasi-colonialism. Egypt was a major power, did their religious beliefs and traditions ever spread outside of Egypt proper? Or even beyond Nubia which was influenced by Egypt
There's some notable overlap between the traditional religion of the Berbers and the ancient Egyptian religion - but it's unclear whether that's due to ancient Egyptian beliefs spreading west, or a common origin for both beliefs in what is now Libya. (The Berbers today are associated most with Morocco, but originally included peoples through eastern Libya.)
Research by William Shaler (19th cen.) and Mohammed Bazma (20th cen.) recite that both Berbers and ancient Egyptians name Ammon as a major god, and Berbers also worshiped (among others) Isis, Set, Osiris and Neith - the latter two are commonly thought to have a Libyan origin (even the ancient Egyptians said that Neith was born in what is today Tunisia). More generally, ancient Berbers worshipped ancestors and the dead, and per Joann Fletcher (and others), the Guanches (a subset of the Berbers) mummified the dead.
Of course all this is just a facet of a larger mixing of ancient deities and religions across the entire Mediterranean and Mesopotamian region, e.g. from the commonly known Zeus/Jupiter to more speculative pairings such as Tannit (Libyan)/Athena (Greek). (See, e.g., Frank Moore, "Canaanite Myth and Hebrew Epic" from Harvard Press.) I don't know of anyone who's done a "definitive timeline" to say which iteration of a god came first and, therefore, who influenced whom - if the same is even possible.
Egyptian religion did permeate throughout the ancient world. But, it only exploded in widespread popularity during the Hellenistic Period.
When Alexander the Great died, his conquests were divided up between his generals, and they formed their own kingdoms. These successor states would consist of Persians, Indians, and Egyptians, but they would be ruled by a Greek/Macedonian upper class.
In these Hellenistic kingdoms, the rulers would adapt local customs to be more Greek-like. The process of Hellenization applied to the Egyptian religion as it did to other aspects of Egyptian life. In Ptolemaic Egypt, the rise of the Cult if Isis is a great example of Hellenization. The Cult of Isis took the animalistic form if the Egyptian goddess and anthropomorphized her to more closely resemble the Greek ideal of the divine. Due to the increased trade networks in the Mediterranean at this time, Egyptian cults like the Cult of Isis spread to parts of Greece and temples can be found in the Roman city of London. There is no doubt Egyptian religion spread throughout the world of antiquity, but it was only after the conquests of Alexander that it gained widespread popularity.
An add on question, if I may.
It is my understanding that many of the basic concepts of pre-Egyptian and Egyptian monotheism became a foundation for the early Israelite and Cannanite belief systems, significantly influencing their development and setting the stage for many christian beliefs. </runon> Am I correct or am I confusing times, places, and religions?