Is evaluating Christian or sectarian websites or those that contain songs and movies, and correcting explicit words as part of my work in search engine optimization for Google, considered assisting in falsehood?

Your work must be within what Allah has permitted. It is not permissible to work on evaluating websites that contain disbelief (kufr), innovation (bid'ah), or immorality (fusooq), because that constitutes aiding falsehood and participating in it. Allah Almighty has said: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression." Furthermore, the one who points to evil is like the one who does it. Therefore, beware of evaluating forbidden websites, even if it leads to your dismissal from work, for whoever gives up something for the sake of Allah, Allah will compensate him with something better.