But with Worf that was his direct parents, and he was brought up by them, and was then transplanted to an entirely different race and planet. There could be an entire thread about the ethics of that.
Birthright is one of my favourite episode(s), at least in season 6 of TNG. Worf was only six years old in 2246 when when his biological parents were killed during the Attack on Khitomer. They had only been living there for a year before the Romulans essentially masacred the Colony, and Worf was one of only 2 survivors, the other being Khalest, a House Mogh "housemaid/nanny". A distress call from Khitomer was recieved by the USS Intrepid, of which Sergey Rozhenko Was Chief Petty Officer. Both Worf & Khalest were rescued by the Intrepid. Sergey adopted Worf and treated him equally to his own son, Nickolai. Worf viewed Nickolai as his Brother.
- Paraphrased from Memory Alpha.
He may have been Initially brought up by his biological parents on Klingon worlds, but only until he was 6. Humans only start forming true memories from roughly this age. Worf remembers being mauled on Khitomer by a beast, and having a pet Targ, though these are lilely his first true memories of his childhood. Its doubtful he would have remembered anything significant about his Klingon heritage before the attack, and even if he did, he would have been too young to understand most of it properly.
Worf was an orphan and him & Kahlest would have almost certainly died if they were left on Khitomer. Hypothetically, if the Intrepid never recieved the distress call, maybe a Klingon rescue party was sent to the Colony to rescue survivors, but we don't know. If Worf & Khalest were rescued by the Klingons, its unclear if they would have been rehomed or even rehabilitated in the first place. Klingon culture may view orphans as having no value, especially as Khalest says to Picard in 'Sins of the Father', that she considered herself "dead" as her house was gone, despite Worf still being alive. Its true that this is also because House Mogh was accused of being the reason for the Khitomer Massacre, but i'm not going to get into that.
Anyhow, Sergey was clearly being compassionate when he adopted Worf. If he didn't adopt him, he would likely have been take to some futuristic foster home anyway. The Federation would never have treated Worf badly anyway, since it was allied with the Klingons, and he was only a small child! The fact that Worf considers Nickolai a father figure as much as Mogh just proves that he and his wife was always treated Worf as an equal.
Worf has mentioned multiple times that he still had trouble adjusting to Human life. At first he wouldn't eat any human meal Helena made so she learnt how to make Rokeg Blood Pie, which Worf greatly appreciated. This clearly shows that they respected Worf's Klingon Heritage and they also allowed him to freely research Klingon culture (they had no reason not to anyway since they were again allies of the Federation). When worf was 13 he was takkng part in his school's soccer championship, and he went to head the ball at the same time as a human child, Mikel. Worf collided with Mikel so violently that he snapped Mikel's neck and the boy died the next day. This had a large impact on Worf and how he viewed humans. He was now old enough to understand that he was living in an Alien Culture and that humans were biologically more fragile than him. Worf then learnt to exercise self-restraint in his daily life, to avoid anything like that from ever happening again.
All of these things are explored in TNG and mentioned further in DS9. There was no reason to further explore the ethical issues of him being rescued as thats what it was. And as much as the 6 year old worf struggled to adapt to human life, he was very young and didn't fully understand what had happened to him. Worf also likely had some buried childhood trauma from Khitomer, which wouldn't have helped his behaviour either.
He was definitely "transplanted" although that is a strange term to use in this context. Considering he no longer had any Klingon family and the Klingons may have just killed him anyway for being of House Mogh, and an orphan, the Federation literally saved his life and Sergei gave him a new family. Not a Klingon family, but as I just said they most likely wouldn't have wanted him anyway. This also is supported by the fact that Khalest is present and allows Sergei to adopt Worf. If there were any Klingon Cultural values or customs being ignored, she wouldn't have given Sergei permission in the first place.
As far as cultural appropriation is involved, worf never claimed anything in human culture to be his own, nor did his human parents do the opposite. That entire argument is rediculous.