Were 20th century Hungarian Jews culturally more Jewish or Hungarian?

Recently watching the film The Brutalist and having Hungarian ancestry. It’s something I’ve thought a lot about. How Hungarian were Hungarian Jews in the early 20th century?

I know because of holocaust a lot of jews lost their faith and that led to a lot of atheist and agnostic Jews living a new life in America. I’m just curious did they bring any of the Hungarian culture with them? Or was that also left behind.