Levin was deep-thinking; Stiva was shallow. It is hard to believe there was long lasting friendship between these two. Exactly What qualities in Oblonsky kept this friendship alive?
Levin constantly chided Stiva for his bad husbandry, but if Oblonsky was as shrewd as Levin wished him to be, would Livin have liked him?
Was not Stiva's silliness or the lack of guile exactly the kind of quality that Levin found most appealing in a friend?
Oblonsky is presented as a person who is everybody's friend. He's not an especially good person, though. He cheats on his wife. He makes a poor deal selling his land. He's not particularly good at his job. The reason he survives is because everyone likes him, but he's not sharp enough (or ruthless enough) to use this likability to his advantage. You probably know someone like him.
Levin, on the other hand, doesn't have many friends. He prefers his farm to the city. He tends to focus on his own affairs, meaning he takes little interest in the affairs of others. He doesn't like small talk. Oblonsky is happy to talk to him, where few others will tolerate him.
In other words, Levin has few friends, while Oblonsky has many. The relationship is asymmetric, but it works because Levin has no one else to turn to. Oblonsky could be smarter, more sober, or better at business, but as long as he's friendly, Levin will be his friend.
Konstantin Dmitrievich Levin, in a way or the other, is a self-portrait of the author Tolstoy himself. So, your question if Levin would have Oblonsky as his friend in real life seems answerable.
In Part 1, Chapter 5, it is mentioned that Levin and Oblosnky were childhood friends,
Levin comes to Oblonsky’s office, interrupting a council meeting. Levin and Oblonsky are friends from childhood, but they have led very different lives.
From the initial chapters (after Levin gets introduced) we instantly understand that Levin is an independent-minded man. Oblonsky is not a man with a great serious emotional depth, he can't settle on any one feeling for very long.
Dolly was no longer attractive and good-looking to Stiva, so to satisfy his shallow emotional urges, even forgetting that he was father of five children (two of them couldn't survive), he went for other women to satisfy his desires and as Tolstoy writes:
He could not at this date repent of the fact that he, a handsome, susceptible man of thirty-four, was not in love with his wife.
All he repented of was that he had not succeeded better in hiding it from his wife.
Levin being independent-minded and socially awkward didn't take that flaw of Stiva's character as a barrier in their childhood friendship. We, accepting Levin as his own person and follows his own vision of things, cannot say of Levin's view on Stiva's adultery in entirety. But even if Levin were to accept the majority's view and holds some group's prefabricated views then also it seems plausible and reasonable why Levin didn't break from Stiva, because Dolly herself didn't break from Oblonsky even after more than one adultery and also none of Scherbatskys shunned Oblonsky, not even an intellectual personality and Levin's own half-brother Sergei Ivanovich didn't consider Stiva's adultery in their friendship, then why would Levin do that?
chided Stiva for being a bad husband, or something along those lines. I disgaree with Hamlet, though - I think this is a question about the author's intentions.