First of all, you seem to believe there is only two possibilities: literal 144-hour creation and evolution. That simply is not the case: there is, for example, the "progressive creation" model. I find the progressive creation model of Hugh Ross, for example, quite compelling, and also quite consistent with a day/age reading of Genesis 1.
Secondly, even if God used macroevolution as His method of creation, I don't believe that excludes the intrusion of sin upon the world. Let's not forget that mankind is endowed with a unique gift that no other animal on the planet has: a spirit. It is this spirit that makes sin possible; it is this spirit that is ultimately redeemed by Christ. Thus, it is conceivable that God used evolution as part of His creation miracle, intervening additionally at the emergence of humankind in order to endow him with spirit, and thus make him accountable for sin.
So no, it is not necessarily contradictory to believe in the necessity of Jesus as redeemer and believe in evolution.
But let us suppose for the sake of argument that it is indeed contradictory. Haven't you ever held contradictory thoughts on other issues before? Of course you have. Have you always been 100% logical and consistent in your thinking? Of course you haven't. Thus, since it is possible to hold contradictory thoughts, it is still possible to believe in both the Bible and evolution. It would be incorrect, but possible.
And thankfully, such a person can still be saved, because God does not require us to be 100% correct on secondary issues of theology and doctrine. He only requires that we place our lives in the hands of His Son.
and because we have done that....when we do that....we want to be obedient....
obedience is still required.