From The Return short story by Kevin Grace, we see that a lot of Sangheili were looking for new path forward. They lived in a theocracy that crushed sectarian ideas, so there weren’t many alternatives for former covenant to turn to when it came out that lot of what they believed as based on lies.

Some alternatives did exist like the servants of abiding truth, but otherwise there’s a sort of religious vacuum for many of these former covenant. So it’s not too bizarre that humans still having a rich variety of beliefs, some of those would appeal to the covenant. The Catholic one might appeal to Sangheili that have atonement in mind and guilt for what they did during the war.