I'm not sure what would be required as proof. It's my understanding that if you state thay you're a now a Christian, you likely wouldn't be admitted. Obviously you could lie, which could get you deported later. If you were admitted, I believe your minor children would be as well.
I've never been Jewish, which is why I think it's wild that I could make aliyah. And even though no one after my grandmother (to my knowledge) was Jewish in my family, I always felt a kinship with Israel and all Jewish people. So when I found out in my twenties that my grandmother had been Jewish, it explained a lot for me. Guess there was some latent spiritual/physical connection of some sort. :)