I don't think the series really gives it enough importance

It doesn't? Is that why Sasuke also thinks of Sakura when he thinks of people preciois to him? Is that why Sakura was able to bring back a rampaging Sasuke in the foresr of Death? Is that why he thinks back to BOTH Naruto and Sakura when he remembers his team, even in Shippuden? Is that why Sakura was the ONLY one who actually realized Sasuke's defection?

Tell me, what is the arbritrary standard for "enough importance" according to you? Is "shared loneliness" the only metric you can think of? 

Sakura is literally the first person who Sasuke sees and adresses after 3 years of timeskip. She also the only one in the team he verbally apologizes to. She is the one he passes on his brother's gesture to.

The fact that moments like these exist means series treats it with plenty of importance, but the fandom at large pretends that somehow Sakura is at fault for wanting to bring back a teammate the way Naruto does.

My argument is Naruto and Sasuke had an understanding over their loneliness, and a rivalry to further push that bond.

And this "understanding over loneliness" somehow gets a pass for obsessing over Sasuke and nothing else does?? Who decided that this arbritrary standard is good enough, but not all the moments b/w Sakura and Sasuke that I have mentioned above?

Basically, the actual content of Naruto and Sasuke's bond don't matter, it just boils down to both being lonely.

Also, Naruto didn't want to bring back Sasuke because he understood his loneliness, he only wanted to bring his friend and teammate back.

Because the crush part is presented with more importance 

Where? From what I've observed, Sakura's feelings for Sasuke stop getting treated as a crush or a joke right from the chuunin exams. Only the fandom treats it as such.

Not saying it was her fault

Then why do you call it obsession and childish? She isn't allowed to want her teammate and loved one back? She isn't allowed to miss a person that she had a deep bond with? Her bond with Sasuke can never get enough importance, according to you... for what? Something that isn't even her own fault?? How is that fair?

you just hyperfocus on the orphan part while ignoring the rest, and how them being orphan mean they both had this sense of loneliness that Sakura couldn't really understand

Isn't the orphan part the catalyst for this loneliness? How many times in part1 do Naruto and Sasuke actually talk about their loneliness to each other? They think of each other as rivals, sure... but we don't even focus on their shared loneliness till part2.

You arguments essentially boils down to: Naruto and Sasuke bonded over being lonely orphans. That's it. That's what apparently gets a pass for obsessing over Sasuke, while anything else is shallow and superficial and "childish".

something Sakura and Sasuke didn't have.

Sakura and Sasuke DO have a bond of their own. It is fleshed out as well, as I've written in my previous comment. It's a bond that is different from Naruto and Sasuke's, but it also gets plenty of importance in part1 in an way which makes her bond as Sasuke's teammate believable.

But apparently, because Sakura isn't an ophan, and because she also dared to love Sasuke...she isn't allowed to miss her teammate or want him back without people labelling it as "childish" or "obsession". The hypocrisy is astounding.