In an alternate timeline where religion was never ended on Earth, the Religious Unionizatoin of Planets was a religio-political coalition established in 2407 as a break-away of several Federation members who felt that their beliefs were threatened by the Federation, in particular President Nechayev and her inner circle.
After religion was officially banned in the Federation, the rogue group known as the New Insurrection was publicized as enemies of the Federation and legal acts of violence were permitted against them. Several members of the Maquis remnant, who were part of the New Insurrection, began preaching that the Federation's only qualms with the New Insurrection were based on freedom of religion.
This escalated until various groups began rising up, proclaiming that the Federation was repressing them by refusing them to adhere to their own religions. When violent actions against these individuals ensued, the Second Catholic Church and the Second Protestant Movement banded together to form the Religious Unionization of Planets.
In the Federation, it is often mistakenly believed that, because certain members of the New Insurrection are religiously mindful, the New Insurrection either started, supported or is in league with the "Union". No official league, however, has been created between the two groups.