Coming from a Catholic, I think being religious (or, at the very least, having religious beliefs) puts you more in a rough spot when it comes to CTB.
Putting aside the toxic culture surrounding most Christian denominations, having faith in God makes you feel shitty for having these kind of thoughts in the first place because you're taught from a young age that God gave you the gift of life—therefore, you'd be ungrateful for "throwing it away." I can't speak for all Christians, but this belief only worsens any CTB-adjacent thoughts because how could you want to waste God's gift? He is benevolent to grant you life, yet you want to throw it away. How ungrateful and selfish! Honestly, I think it's this belief that led to the idea that people who commit CTB are selfish.
Not only that, but there's also spiritual consequences to CTB. Going through with it is a one-way ticket to Hell. There's no ifs, ands, or buts. God doesn't care if you're depressed, neurodivergent, queer, or what have you; all that matters is you CTB and that means you wasted God's gift, so to Hell you go.
Being religious keeps you alive, sure, but it doesn't remedy the depression, anxiety, and other issues driving you to want to CTB in the first place. Because of that, you're essentially forced into limbo: you want to die, but you're scared of being ungrateful and suffering from eternal divine punishment.
Still, this is my perspective on the matter, so other people's are bound to be different, even yours.