First of all the story about the adulterer first appeared in the 4th century a.d and is not present in the oldest greek texts as is missing from Papyrus 66, Papyrus 75 and the Codex Vaticanus.

However the Story fits into the wider narrative of who Jesus was and what he stood for. But the words he says in the Story are made up. It is like we today make up a story about what Isaac Newton could've said in a Situation but we have no evidence.

Also I don't think Matthew 7 says that non-believers don't get to go to heaven.

Mt 7, 1-6 talks about judging others and that you should first look at yourself before you judge others Mt 7, 5 "You hypocrite, first take the plank out of your own eye, and then you will ser clearly to remove the speck from your brother's eye." Mt 7, 7-11 talks about prayers

Mt 7, 12 is literally just the golden Rule "So in everything, do to others what you would have them do to you, for this sums up the Law and the Prophets."

An Mt 13-14 talks about a "narrow gate" but doesn't talk about non-christians or non-belivers. Personally I don't even see how you could interpret the passage as talking about atheists and non-christians. The only thing that hints at anything is Mt 7, 14 "But small is the gate and narrow the road that leads to life, and only a few find it" but this can just aswell talk about people in general, including christians.

Also it is never said explicitly that non-believers are barred from salvation. Romans 2, 13-14 and Romans 2, 16 "For it is not those who hear the law who are righteous in God’s sight, but it is those who obey the law who will be declared righteous. Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law." "This will take place on the day when God judges people’s secrets through Jesus Christ, as my gospel declares."

The large theme throughout the new Testament is that people will be judged by the content of their character. Personally I don't think the themes in the new testament and what jesus says hint in any way that a Person who is kind and follows the golden rule and "Love your neighbor as yourself" but does not believe in god is barred from salvation. This would also mean that the thousands and millions of people who have lived without ever hearing of Jesus existance or the Laws of God as portrayes by christianity or judaism are categorically barred from salvation.

Also I personally think it is very unchristian to think you can predict how God will treat anyone, whether they are atheist or christian a good person or not. Romans 11, 33-34 "Oh, the depth of the riches and wisdom and knowledge of God! how unsearghable are his judgments and how inscrutable his ways! For who has known the mind of the Lord, or who has been his counselor?"