Is it religiously permissible for a wife to remain with her husband who curses religion, does not observe prayers, and negatively impacts her religiosity, especially given the presence of children and the consultation of some scholars who advised leaving him if he persists in his ways?

Anger does not negate accountability unless one completely loses their mind. If the husband is aware of what he is saying when he insults the religion, do not allow him conjugal access and do not live with him until you present your case to a Sharia judge or trusted scholars. If he is excused, then the marriage bond remains. As for his abandonment of prayer, it is a grave matter and a great sin. If he repents and becomes righteous, then praise be to Allah. Otherwise, it is better for you to separate from him, due to the harm that remaining with him poses to you and your children. Seeking a divorce in this case is recommended and not a matter for istikhara.