I believe if we look at being self righteous in literal terms,anyone who is self righteous cannot be a Christian.
The righteousness of Christ in us has called for us to love one another,as Christ loves the Church.
Here is a example:James ch 2
If ye fulfil the royal law according to the scripture, Thou shalt love thy neighbour as thyself, ye do well:
[9] But if ye have respect to persons, ye commit sin, and are convinced of the law as transgressors.
[10] For whosoever shall keep the whole law, and yet offend in one point, he is guilty of all.
[11] For he that said, Do not commit adultery, said also, Do not kill. Now if thou commit no adultery, yet if thou kill, thou art become a transgressor of the law.
Being self righteous would imply that a person keep his own salvation by his or her righteousness,not the Grace of God through Christ Jesus.