In the beginning it prosecuted the Christians but later the Roman empire embraced Christianity and imposed all through the empire. https://en.wikipedia.org/wiki/Christianity_as_the_Roman_stat...
christianity offered a unifying thematic message and de facto polity under which constantine believed he could more effectively maintain power and peace. this system was ripe for corruption but now the people are generally kept in line by the conflation of church and state.
islam arises primarily as a repudiation of polytheism and what is perceived as loose monotheism and nonviolently sweeps through the area quickly.
regional leaders quickly learn the same lesson that constantine learned and use islam to prevent rebellion and exert control, with the added lesson learned that it’s best to just ensure everyone follows the same code from the start so that you don’t have to do a lot of political cleanup in the transition to a new belief system.
fractured “european” leaders realize how much power they’ve lost and decide that they should unify under the christian brand to go take back their power.
and the cycle goes on and on
I doubt that “repudiation” of said things was the main driver.
I’m pretty sure by 600ad Rome was pretty solidly Christian (or at elite levels, perhaps secular), what other gods did exist were folk/syncretistic practices, which also existed in Islam (sufis, Zoroastrian stuff, gnostic stuff etc) and which still existed today in Christianity (in the Philippines, the Caribbean, Africa, etc)