If God judges people of other faiths justly, why should I try to convince them of Islam?

Because you yourself are meant to be truthful. Whoever sincerely holds something to be the truth must pass it on, or they are not being honest with themselves. Judging others remains with God.

It is true that God judges every person justly. Whoever sincerely believes in something will be treated by God as a sincere person. But it does not follow that we ourselves may stay idle.

The question mixes up two roles. Judging others is God's business, not ours. We should not act as though we were God, but as human beings. And as human beings we are responsible first of all for ourselves. Each of us must be our own judge.

This is the heart of the matter. Whoever holds something to be the truth and is truly convinced of it cannot keep it to themselves without being untrue to themselves. The very sincerity that God recognises in others requires us to pass on the truth we have recognised. Whoever stays silent despite being convinced is not being truthful with themselves.

The verses above show how this should be done. There should be people who invite to goodness. They do it with wisdom, kind exhortation and the best arguments. And the last verse reminds us that one is only an admonisher. One invites, explains and shows. Whether someone accepts is their own decision, and the judgement remains with God.

So both thoughts belong together. God judges every person justly, and precisely for that reason everyone who believes should honestly pass on what they have recognised as true.