Nobody Comes to the Father Except... or Should It be Accept?

When Jesus says "No one comes to the Father except by me" and "I am the way, the truth, and the life," and when it is claimed that through Jesus, all are saved, does one have to believe in Jesus for these statements to be true?

While a lot of moderate and Liberal Christians, as well as atheists and people from other religions are happy to hear that the current Pope is not so negative and narrow-minded as some previous Popes, many Conservative Christians and Evangelicals seem to be upset by this Pope's tolerance and potential inclusivity.

All things fall because of gravity. If I don't believe in gravity, does gravity stop being true? If I don't believe in viruses or bacteria, will I then be free from illness?

Can't Jesus present an atheist to the Father quite as easily as He can an Evangelical, or a Catholic, or any other flavor of Christian? Does coming to the Father by way of Jesus any less true because someone does not believe in Jesus. Wouldn't that make grace even more... graceful... by Jesus welcoming even those who never believed in Him, or even campaigned actively against Him, and presenting those people to His Father, who is also the Father of us all, believers and non-believers alike?

I think it's time for Christians to stop pretending as if they are in some exclusive club, and it is certainly time for Christians to stop pretending as if they are on the Membership Committee of that club.

Whether or not God does in fact welcome all is irrelevant, because God has made it clear to me that I am to welcome all -- and I have a hard time accepting that God would ask something from me that He would not do Himself.