What is in Islam and Christianity that is similar to the above?
I won't speak on behalf of Christianity because my knowledge is limited, however before saying anything it is better to clarify that I don't hold authority over Islamic knowledge too, so whatever I say reader's discretion is advised
"When there is incest, adultery, atheism, hatred of religion, no more dharma, and sin everywhere, the impossible Iron Age has come; in what way the world will be saved? For the helpless, the Lord Himself will manifest as the Supreme Purusha. He will be called the Kalki incarnation and will be glorious like a lion coming down from heaven."
Being Muslim our belief is that in age of Dajjal (AKA Anti Christ), most of the people will be far away from religion (no religion professes adultery, or sins, or unnatural practices) before he appears people of faith will face so much hardship practicing their religion that they would prefer to leave and settle in forests and mountains away from civilization and would prefer being sheepherders. And when the Dajjal appears his major followers would be dancing women, musicians and he would show such charms and attraction that even the most devout of Muslims may mistake him to be true in what he is claiming. Incest, adultery, atheism being hateful of religion will make his work easy to make people accept that he is the (false) GOD, whereas he is the liar and whatever powers he would hold to impress people would be because of GOD's will. With him all these incest and bad practices will rule, he will spare people and reward them who agree to him being the GOD and will kill the ones who won't agree. He will rule most of the world and Imam Mehdi's Army will fight him and Jesus A.S is the one who will kill him and get the world rid of his evil, lies and falsehood and will restore peace and order back to the world.
The point to note here is division of the world into two clear groups followers of Dajjal (the liar and evil) and people fighting that liar's forces under command of Imam Mehdi and then Jesus. So who so ever believes in Jesus he will automatically follow his religion.
There is a lot detail to it, prophecies and events happening before and after appearing of this Dajjal, which I have skipped for purposes of keeping my reply short and to the point.
(Like before end of times and Judgment day adultery and sex will be so common that people won’t feel ashamed of it while professing it openly in streets, without any privacy.)
(Like Jesus will also fight gog magog creatures who will make living difficult for humankind and will consume all our resources)
"The mission of Kalki Avatara is to re-establish the religious principles, which have disappeared by the end of Kali Yuga, the iron age of hypocrisy and quarrel."
Same as I said would happen once Jesus A.S has killed the Dajjal and defeated his forces, he will go on to make practice of the religion (which we believe to be Islam) easy for people and will restore peace and prosperity again. Those times would be the just times, people will be healthy, happy and will prosper.
"He'll simply go on killing all these non-believers, Godless creatures and usher in another Satya-yuga, the golden age of righteousness and truth."
As above
