"What makes rulers and societies to convert to faiths from outside. Some recent interesting work done on this issue is by Alan Strathern, a historian on the history of religion.
According to Strathern, the religions of the world can be divided up into two categories - immanent and transcendental. (This division is far form perfect, which I will get to later) - immanent religions can be roughly understood as the default state of religion, widespread in all societies around the world. These are the religions that has essentially sprung from animism, which attributes supernatural causes behind natural phenomena, explain why the world is as it is, and who also control fortune. In these religions you would sacrifice and worship the gods in the hope of receiving benefits in this life - a good harvest, a good marriage, victory in battle, etc.
Transcendental religions on the other hand have not always existed, but started to appear in the world during Antiquity. In these religions, the "supernatural" is not just a way to explain phenomena or to derive benefits in this life. It is the fundamental logic according to which the universe and daily life works, and it becomes a core aspect of the identity and moral systems of societies and individuals.
When you worship deities in these systems, you don't just hope for a good harvest of victory in battles. You are first and foremost looking for benefits in the next life - going to Heaven and avoiding Hell, as a Christian or Muslim, or achieving Nirvana and avoiding rebirth in Buddhism for instance.
This means that these religious systems become much more resilient in the face of outside opposition because leaving these systems means shedding much of your previous identity, both at the individual and societal scale. For kings, this meant that converting to a new faith would be severely damaging to their legitimacy, and risk them being deposed. For individuals, it meant they would essentially lose their social life and face social ostracisation and excommunication.
Notably, this is not the case with immanent traditions. Here, converting to a new faith is not really considered morally unacceptable. When Norse Pagans converted to Christianity for instance, they gained new benefits - socially and politically - while they didn't feel they lost much in the afterlife, because promises of a good afterlife were not really a significant part of their religious practice anyway, and their previous religion did not involve a build-in condemnation of converting to new religions.
In contrast, transcendental religions such as Christianity and Islam have a strong built-in defense against apostasy, which is condemned morally in both of them, and Christian and Muslim societies have punished apostasy both in this life and the next.
This of course raises the question: Which religions are transcendental? Strathern had his starting point in Theravada Buddhism, researching why Buddhist societies in South and Southeast Asia proved resistant to Muslim and Christian conversion efforts in the 17th century - in particular in Sri Lanka and Thailand. The theory being that Buddhism represented a significant power structure both in society and in daily life - kings resisted conversion, even when it would confer them political advantages such as European economic and military aid, because it would cause popular discontent and harm their legitimacy as rulers of the state.
Taking the broader perspective, when you will look at a world map, you can see that pretty much all significant populations that are not Christian and Muslim live in Asia, namely in India, mainland Southeast Asia, China, Korea and Japan. Although syncretic beliefs and folk beliefs still persist in much of Africa and Latin America, they are often meshed with Christianity or Islam, which are by far the dominant beliefs in this region.
As such, the primary religions that have proven resilient in the face of monotheistic conversion are Buddhism, Hinduism, and then the collection of Far Eastern religions - Shinto, Korean Shamanism, Chinese folk belief (Strathern puts Neo-Confucianism in China as a transcendental belief, which is something I somewhat disagree with)
As such, the main beliefs that have resisted Abrahamic expansions are located in Asia, and have the advantage of being the defining beliefs of developed, powerful societies in these regions. By the time they were faced with monotheism, they already had centuries of built-in resistance against outside attempts at conversion, a resistance that would sometimes turn violent, if necessary. (Note that this doesn't necessarily mean the religions were categorically intolerant - in contrast, Theravada Buddhists and Hindus had a place in their worldview for other religions, they just could not allow them to be dominant)
In contrast with Christianity and Islam however, Buddhists and Hindus, nor Confucianists, did not really have proselytization as a core value of their religion (Buddhists were on occasion missionaries, especially in the early history, but to the extent of Christians and Muslims) - this might help explain why their spread outside their original core areas in Asia were relatively limited.
As such, a large part of the success of Christianity and Islam can be attributed to these things - a built-in resistance and opposition to other faiths, a strong sense of proselytization, and finally, the support of powerful states who made it a priority to spread the faith. And in most of the world outside of Asia, Christian and Muslim missionaries found a fairly receptive environment of immanent traditions, who didn't have a built-in opposition to outside faiths in their belief systems.
Its had to make a full answer to such a broad question, but I hope I have helped show you a way to think about this issue at least, even if I don't thing Strathern's conclusions flawless.
I recommend reading some of his work such as:
Unearthly Powers: Religious and Political Change in World History (Cambridge 2019)
Kingship and Conversion in Sixteenth-Century Sri Lanka Portuguese Imperialism in a Buddhist Land
Thailand's First Revolution? The role of religious mobilization and ‘the people’ in the Ayutthaya rebellion of 1688"
