There is a lot of evidence that says that early Jesus followers didn't believe Jesus was the literal son of God ('son of God' was more of a title, for instance it was used to refer to Caesar), and didn't believe he rose from the dead (a lot of early texts don't talk about his death, since it was so shameful). Instead, the early communities focused on Jesus's message about how the world was wrong, but a better one was on the horizon, and we could all do our part to bring it about.
Thus, I would say that although a lot of religion would be different, it would not be altogether missing. People believe in God not because people tell them to, but because God tells them to; if you're assuming that God doesn't exist, then no amount of backwards time travel is ever going to help us learn more about him.
That said, I would assume religion would be a lot less dogmatic (not sure if that's the right word), and a lot more spiritual. Meditation works, as does a lifestyle free from worldly pleasures. These things have demonstrable effects, and some people attribute them to the divine; on the other hand, there's no real evidence to support hating gay people, so that probably won't make the cut.
The only other option I can think of is that backwards time travel isn't something everyone will do. Poor people won't have the ability to, and people firmly fixed to their beliefs may be too afraid to be proven wrong to try it. So, in that case, a lot of modern religion will persist.
EDIT: Come to think of it, I would love it if this happened, and I think a lot of intelligent religious people would too. People who don't take the Bible literally really want to know what actually happened; to be able to hear Jesus speak would be like hearing Socrates speak, an absolutely priceless experience that could help fill in the gaps of history, and end the debates once and for all. With the ability to hear the prophets and founders of every religion, I think believers would become closer to one another, as they no longer would have to fight over what they think is right.