Sorry for the long explanation, you hit the button, but no, that's a misconception because people have piss poor reading comprehension and, I suspect for some, legit hate women and/or Zelda respectfully(there is a very weird subset of BotW/TotK fans who loathe Zelda) and are perfectly willing to mischaracterize her actions. Also, to be completely fair, some people just felt like it was their house, not Link's, and were angry that Nintendo "took" it from them and changed it and proceded to take that ire out on Zelda for some reason, and I do have to admit that the joke is a little funny in a vacuum, so some casual players weren't motivated to look deeper even if looking deeper would immediately prove this theory wrong. (Also no shade to the shippers as a whole they are lovely and I would die for them, but there were some rare but very vocal Link/Sidon fans who got real fucking mad about Nintendo ruining their gay ship and giving Zelink some validation and painted Zelda as an asshole to cope :/)
But yeah she didn't steal it, and assuming she did is an insanely bad-faith read of Zelda's character and the situation as a whole.
To start off with the basic stuff, while the house is referred to as "Zelda's" only by the NPCs in town, apparently in the original Japanese they call it "the place the princess is staying" which does not imply ownership. I also don't recall the exact wording right now but I believe in Zelda's diary she does not talk about the house like she owns it, the only place she says is her own is the added study which apparently she commissioned herself, so not even Zelda thinks of the entire home as her's, just the room built specifically for her use, and she even canonically lets Link hang out there with her as his old hair tie is in there.
And going deeper, if you actually think about the characters and their personalities and relationship dynamics and how the game conveys all that through the story and the game mechanics themselves it is VERY clear that Zelda and Link live there together because...
1) Link(and thus the player) cannot mechanically sleep in beds he does not own or is not renting, you can't just walk into any old house in town and crash in a random bed, you have to rent them at Inns and Stables, and the only beds that are free to sleep in are the ones in the new house you can build in Terry Town and the one in Link's original house where Zelda is staying. This implies both are using the bed, or at least share the house as equals.
1.2) The game def also wants you to use it's terrible house building mini game, so they try to intentionally shift focus away from the Hateno house as Link's base to the Terry Town one, and that's also why the weapons displays/decorations in the original house are gone. They want you to use the new ones and tbh the weapon displays would look dumb empty but they also can't just give the player really op weapons right away which is what most players put up in there, so they're replaced by nice photos of the landscape. And also, if you have some imagination, you can pretty quickly come to the conclusion that if Link brought Zelda there after rescuing her he might take the weapons down so as not to remind her of violence while she's trying to heal from 118 years of Trauma.
2) There is a continuous running gag in both BotW and TotK where most people just don't know who Link is at all. He has dialog options where he can outright say he's the hero of legend and show off the sword that proves it and people don't believe him because he's short and unassuming. The only people who always recognize him are close friends and Sheika(as well as the Yiga Clan who want him dead), but even the mayor of the town Link lives in doesn't know who he is. So of course the villagers don't refer to it as "Link's house" or "The place where the Hero and the Princess are staying" because they canonically don't know who tf he even is. (And again, imagination, is it going to be a big deal if the Princess and future Queen of Hyrule is living completely alone with a man she's not married to? PROBABLY.)
3) Assuming she stole the house, while yeah, again, slightly funny in a vacuum, does go completely against Zelda's characterization as a profoundly kind and selfless person who would never just presume ownership over anything. Link himself would probably give her the house without question if asked because he is characterized as completely devoted to her, but there is no world where she would ever "steal" something that rightfully belonged to anyone, least of all Link.
4) If you complete the BotW DLC you get a picture of the champions + Link and Zelda from the past, and that ends up on the nightstand in the house if you buy it. If you play TotK on the same account as the one you beat said DLC in you can transfer over certain things like your horses...and that picture. It's still up in the house after Zelda moves in, and sure she'd have no reason to take it down as it would have sentimental value to her as well, Link put it there and it isn't removed, again implying he has control over the decor.
I could go on but hopefully that's enough. Zelda did not steal Link's house, he probably invited her there because she was traumatized after being rescued and didn't really have anywhere to go that people wouldn't be paying insane amounts of attention to her, and after things calmed down they continued sharing the home while the town had amnesia about Link's existence and neither he or Zelda corrected them because who cares and also potential scandal. People just love taking a joke seriously and refusing to give female characters even the smallest benefit of the doubt before assuming they are selfish monsters for something they straight up did not do.
Sorry again for the rant also I just care about this a lot T-T I know Zelda isn't real but like come on. Fandom has got to stop doing a misogyny all the time.
