Yes, that's the basis for Christianity, belief in Christ's death and resurrection as atonement for sin and reconciliation to God. Jesus said "I am the Way, the Truth and the Life; no one comes to the Father except through me" -John 14:6 

Not sure what you mean by a caste system still exists. One of the basic principles is every person is considered to be loved by God, and salvation (forgiveness of sin) is available to those who believe and accept that Jesus died for their sin. If those aren't your beliefs, then you aren't an adherent to the Christian faith. No caste system. No one is blocking them from belief and inclusion in Christianity but the person themselves. The Bible says there are not to be different levels of salvation or that some people are not allowed to receive salvation even if they believe in Christ as their savior.

Someone who doesn't believe is not lower caste or irredeemable. They simply don't choose to take part in the faith. They can change their mind.