Posting because I just found out the surprising fact that some states have laws on the book that prevent atheists from holding elected office.
I assume you are discussing the supreme court nominees, and the only thing that I have heard is the pretty valid complaint that one of them has made some concerning comments in the past with respect to separation of church and state.
It's OK to be religious. It is not OK to force your religion on others, especially when your religion (Catholicism) represents a minority (<20%) of the US population.
The article is more nuanced than the headline. If you're just reading headlines, though (because you're skimming a news aggregator, say), then you get the idea that people think she can't be a Supreme Court justice because she's Catholic. Down in the article, you find that people think that she can't be a Supreme Court justice because they think it's problematic the kind of Catholic that she is. (Or at least because of the political implications of the kind of Catholic she is.)
That's coming from people in office, not just from random crazies on Twitter.
"Judges cannot—nor should they try to—align our legal system with the Church's moral teaching whenever the two diverge. They should, however, conform their own behavior to the Church's standard. Perhaps their good example will have some effect," the paper [by Coney] concluded.
When asked during the 2017 Senate hearing how she would weigh her faith with her responsibilities as a judge, Barrett said, "It's never appropriate for a judge to impose that judge's personal convictions, whether they derive from faith or anywhere else on the law."
https://www.newsweek.com/what-has-amy-coney-barrett-said-abo...
The complaints about her have been purely about her political views and never about her religion directly.