Amy Coney Barrett's father was appointed as legal counsel for the People of Praise--a Catholic weirdly charismatic religious group. There are ongoing concerns about hushed-up issues regarding sexual abuse in PoP (a Catholic group, so no surprise there, sad to say). So, plenty there to be concerned about. But there is no tie between PoP and NAR.

Here is a link to an article from the Guardian to see more info on her father and PoP.

https://www.theguardian.com/us-news/2024/jan/29/amy-coney-barrett-father-christian-sect-controversy