There is not a time in my 80 years of life that I am able to remember that I do not recall that song (What Can Wash Away My Sins) being sung periodically. Not every service of course but on a fairly regular basis. I still enjoy singing it & it doesn't get Old.

Here, of course, we find the statement that the animal sacrifices which were a commandment did not actually take away the sins of the people. The Sacrifice of Jesus on the cross forgave the sins of those who had lived Godly previously & would forgive the sins of those who would obey him afterward.

Heb 10:1  For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect. 
Heb 10:2  For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins. 
Heb 10:3  But in those sacrifices there is a remembrance again made of sins every year. 
Heb 10:4  For it is not possible that the blood of bulls and of goats should take away sins.

Jesus himself made this statement during his ministry;
Joh 14:6  Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra