No, they should not, as everything necessary to salvation is found in Christ. To seek salvation through good works is a denial that Christ is the only Redeemer and Saviour.
“We know that a person is not justified by the works of the law, but by faith in Jesus Christ. So we, too, have put our faith in Christ Jesus that we may be justified by faith in Christ and not by the works of the law, because by the works of the law no-one will be justified.” (Galatians 2:16)
Popular religion thinks that you have to be a ‘good’ person in order to deserve God’s favour. So people tend to assume that Christianity is somehow about living a good life (by obeying the Ten Commandments, or the Sermon on the Mount) in order to please God. They could not be more wrong.
Justified by faith in Christ
The Jews had possessed the law for over a millennium – and had proved its inadequacy as a means of salvation. If we were capable of making ourselves righteous, there would have been no need for Christ to die (Galatians 2:21), and all His sufferings would have been pointless.
The fact that we make no contribution at all to our salvation means that absolutely anyone can be saved, at any time in their life – even as they are dying (Luke 23:39-43).
Not by the works of the law
We are saved not by faith ‘plus’ something (such as baptism, good deeds or religious observances) – but by faith on its own. In his letter to the Galatians, Paul was fighting against those who wanted to impose circumcision on Gentile converts, as something ‘essential’ for their salvation. But if we attempt to ‘add’ any righteousness of our own, we cannot be relying entirely on Jesus.
A so-called ‘gospel’ that includes any element of self-justification is an insult to God (because we are rejecting and despising His free gift), implies that even Jesus was inadequate to be our Saviour, and undermines the very foundations of Christianity (Romans 11:6).
God, our Judge and Saviour,
teach us to be open to your truth
and to trust in your love,
that we may live each day
with confidence in the salvation which is given
through Jesus Christ our Lord. (Collect for 18th Sunday after Trinity)