We are being saved from exactly the same thing as Noah and his family were saved from....not the world and its evil, but from God's wrath upon them, because of it.
As we await the final judgment of this world, we must be certain of our position before God. We must have built our own "ark" which the apostle Peter equates with our baptism.....speaking of the angels who sinned...."who formerly were disobedient, when once the Divine longsuffering waited in the days of Noah, while the ark was being prepared, in which a few, that is, eight souls, were saved through water. 21 There is also an antitype which now saves us—baptism (not the removal of the filth of the flesh, but the answer of a good conscience toward God), through the resurrection of Jesus Christ", (1 Perter 3:20-23 NKJV).....so, we can be saved through the 'water' in a vessel that God has helped us to build by giving us the explicit instructions on how to go about it. The problem is, like Noah's day, the majority don't believe that it is going to overtake them. And those on board this ark have to do what Noah did and put in the effort to work for their own salvation, and to reject the elements of this world that corrode the conscience, namely violence and immorality. But like the Israelites were constantly told to do....we must also steer clear of false worship. The challenge is to identify it in a world deceived by the devil. (1 John 5:19) The "god" of this world can make the truth seem like a lie and vice versa....(2 Corinthians 4:3-4)...but he can only deceive those who don't believe the truth.
God doesn't save anyone, but he teaches us to save ourselves by a complete separation from the goings on of this world, in strict obedience to the teachings of his son...our King, redeemer and judge, who warned us....."But as the days of Noah were, so also will the coming of the Son of Man be. 38 For as in the days before the flood, they were eating and drinking, marrying and giving in marriage, until the day that Noah entered the ark, 39 and did not know until the flood came and took them all away, so also will the coming of the Son of Man be." (Matthew 24:37-39)
It's not that the people didn't know what Noah was doing or why he was doing it, but they chose instead to ridicule him and ignore his message.
Not a soul outside of the ark survived God's judgment on that world....
So who do we imagine is going to survive God's wrath on this present world.....?
Again Peter warns...."Therefore, since all these things will be dissolved, what manner of persons ought you to be in holy conduct and godliness, 12 looking for and hastening the coming of the day of God, because of which the heavens will be dissolved, being on fire, and the elements will melt with fervent heat? 13 Nevertheless we, according to His promise, look for new heavens and a new earth in which righteousness dwells." (2 Peter 3:11-13) Who will enjoy the righteousness of the new earth, if they cannot avoid the unrighteousness of this one?
Our survival depends upon our obedience to God in all things, not just the convenient stuff.....